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Reinsurance Analytical Report for 3000 words answering all questions as per pdf instructions.

Pablo Benito Cano
Year
2011
Description
Panasonic Corporation – Tsunami
Nissan Japan – Tsunami
Fukushima Employers’ liability – Tsunami
Toyota Corporation – Tsunami
Super Dry Corporation – Tsunami
Sky New Zealand – Earthquake
Next New Zealand – Earthquake
Macys New Zealand – Earthquake
Christ Church Council NZ – Earthquake
House damage – NZ – Earthquake
Sony Thailand Floods
Dell Thailand Floods
Daimler Thailand – floods
Thai Hotel – Floods
Thai Resorts – floods
Abayomi
Ibrahim Awe
Claims 1
Claims 2
75.560.000
68.004.000
66.450.000
59.805.000
Est. 162,957,390Est. 162,957,391
78.665.000
70.798.500
67.500.000
60.750.000
56.260.000
50.634.000
62.275.000
56.047.500
86.900.000
78.210.000
69.600.000
62.640.000
45.000.000
40.500.000
55.200.000
49.680.000
66.260.000
59.634.000
67.275.000
60.547.500
56.900.000
51.210.000
62.622.000
69.580.000
2012
Anglo American – Fire South Africa
2013 Nestle Contamination – Swiss
City University London Fire
2014 Oil Rig Explosion Texas US
Wal-Mart Superstores Fire – USA
2015 Afgan Hotel – Terrorism
Brazil Sugar Corporation – Fire
Mississippi Holdings – Hurricane Patricia
New Orleans Motors – Hurricane Patricia
2016
Macys – Flooding Hurricane Patricia
Schefenacker, Germany fire loss
Toshiba Corporation – Japan Fire
2017 Nikon Japan – Fire
Grenfell Tower – Fire
British Telecom – Fire
2018 John Lewis – Fire
Total FinaElf France Pollution liability
ANZ New South Wales Australia – Fires
Australia Famers Union – Bush Fire
Associated News Papers Australia – Bush Fire
SASOL SA Environmental Pollution South Africa
Grenfell Lawsuit
Mitsubishi Motors Japan – Earthquake in Yamagata
Sony Japan – Earthquake in Yamagata
2019 Japanese Power Company – Earthquake in Yamagata
Walmart USA – Fire
Ford Motor Co – Fire
Petronas Mozambique – Cyclone Idai
Ariston Zimbabwe – Cyclone Idai
Tanganda Tea Estate – Cyclone Idai
34.000.000
30.600.000
61.460.000
55.314.000
40.347.000
44.830.000
70.920.000
78.800.000
71.650.000
64.485.000
81.350.000
73.215.000
41.148.000
45.720.000
36.260.000
32.634.000
68.275.000
61.447.500
76.900.000
69.210.000
62.640.000
69.600.000
55.560.000
50.004.000
56.450.000
50.805.000
23.949.000
26.610.000
33.720.000
30.348.000
41.340.000
37.206.000
39.154.500
43.505.000
70.200.000
63.180.000
75.200.000
67.680.000
53.000.000
47.700.000
Est. 65,750,000 Est. 65,750,001
Est. 46,400,000 Est. 46,400,001
68.500.000
61.650.000
58.225.000
52.402.500
88.400.000
79.560.000
66.500.000
59.850.000
60.225.000
54.202.500
23.200.000
20.880.000
37.400.000
33.660.000
29.500.000
26.550.000
Samsung Mozambique – Cyclone Idai
Standard Bank – Malawi – Cyclone Idai
Wembledon Covid-19 Business Interruption Loss
Olympics Cancellation Covid-19 BI Losses
2020
Gjerdrum landslide Loss – Norway
Maersk Essen 750 containers lost overboard
BAA Covid-19 Business Interruption Loss
BP Explosion USA
Novatis – Severe convective Euro storms in June
BMW – Severe convective Euro storms in June
2021
Airbus – Severe convective Euro storms in June
AC Milan – Severe convective Euro storms in June
Fire Marfin Bank Greece
Fire Central World Shopping Mall Thailand
18.225.000
16.402.500
40.950.000
45.500.000
144.000.000 129.600.000
73.400.000
66.060.000
65.500.000
58.950.000
180.000.000
200.000.000
52.200.000
46.980.000
63.400.000
57.060.000
36.260.000
32.634.000
68.275.000
61.447.500
75.900.000
68.310.000
56.340.000
62.600.000
60.500.000
54.450.000
44.302.500
49.225.000
Student 3
Student 4
Student 5
Student 6
Student 7
Student 8
Claims 3
Claims 4
Claims 5
Claims 6
Claims 7
Claims 8
70.724.160
72.845.885
79.338.000
71.026.400
71.782.000
73.671.000
62.197.200
64.063.116
69.772.500
62.463.000
63.127.500
64.788.750
Est. 162,957,392 Est. 162,957,393
Est. 162,957,394 Est. 162,957,395
Est. 162,957,396 Est. 162,957,397
73.630.440
75.839.353
82.598.250
73.945.100
74.731.750
76.698.375
63.180.000
65.075.400
70.875.000
63.450.000
64.125.000
65.812.500
52.659.360
54.239.141
59.073.000
52.884.400
53.447.000
54.853.500
58.289.400
60.038.082
65.388.750
58.538.500
59.161.250
60.718.125
81.338.400
83.778.552
91.245.000
81.686.000
82.555.000
84.727.500
65.145.600
67.099.968
73.080.000
65.424.000
66.120.000
67.860.000
42.120.000
43.383.600
47.250.000
42.300.000
42.750.000
43.875.000
51.667.200
53.217.216
57.960.000
51.888.000
52.440.000
53.820.000
62.019.360
63.879.941
69.573.000
62.284.400
70.235.600
64.603.500
62.969.400
64.858.482
70.638.750
63.238.500
71.311.500
65.593.125
53.258.400
54.856.152
59.745.000
53.486.000
60.314.000
55.477.500
65.126.880
67.080.686
73.059.000
65.405.200
73.754.800
67.840.500
31.824.000
57.526.560
41.960.880
73.756.800
67.064.400
76.143.600
42.793.920
33.939.360
63.905.400
71.978.400
65.145.600
52.004.160
52.837.200
24.906.960
31.561.920
38.694.240
40.720.680
65.707.200
70.387.200
49.608.000
Est. 65,750,002
Est. 46,400,002
64.116.000
54.498.600
82.742.400
62.244.000
56.370.600
21.715.200
35.006.400
27.612.000
32.778.720
35.700.000
31.960.000
36.040.000
33.150.000
59.252.357
64.533.000
57.772.400
65.147.600
59.923.500
43.219.706
47.071.500
42.140.200
47.519.800
43.709.250
75.969.504
82.740.000
74.072.000
83.528.000
76.830.000
69.076.332
75.232.500
67.351.000
75.949.000
69.858.750
78.427.908
85.417.500
76.469.000
86.231.000
79.316.250
44.077.738
48.006.000
42.976.800
48.463.200
44.577.000
34.957.541
37.529.100
34.084.400
38.435.600
35.353.500
65.822.562
70.664.625
64.178.500
72.371.500
66.568.125
74.137.752
79.591.500
72.286.000
77.669.000
78.514.900
67.099.968
72.036.000
65.424.000
70.296.000
71.061.600
53.564.285
57.504.600
53.893.200
56.115.600
56.726.760
54.422.316
58.425.750
54.756.500
57.014.500
57.635.450
25.654.169
27.541.350
25.811.700
26.876.100
27.168.810
32.508.778
34.900.200
32.708.400
34.057.200
34.428.120
39.855.067
42.786.900
40.099.800
41.753.400
42.208.140
41.942.300
45.027.675
42.199.850
43.940.050
44.418.605
67.678.416
72.657.000
68.094.000
70.902.000
71.674.200
72.498.816
77.832.000
72.944.000
75.952.000
76.779.200
51.096.240
54.855.000
51.410.000
53.530.000
54.113.000
Est. 65,750,003Est. 65,750,004 Est. 65,750,005Est. 65,750,006 Est. 65,750,007
Est. 46,400,003Est. 46,400,004 Est. 46,400,005Est. 46,400,006 Est. 46,400,007
66.039.480
70.897.500
66.445.000
69.185.000
69.938.500
56.133.558
60.262.875
56.478.250
58.807.250
59.389.500
85.224.672
91.494.000
85.748.000
89.284.000
90.168.000
64.111.320
68.827.500
64.505.000
67.165.000
67.830.000
58.061.718
62.332.875
58.418.250
60.827.250
61.429.500
22.366.656
24.012.000
22.504.000
23.432.000
23.664.000
36.056.592
38.709.000
36.278.000
37.774.000
38.148.000
28.440.360
30.532.500
28.615.000
29.795.000
30.090.000
17.058.600
42.588.000
134.784.000
68.702.400
61.308.000
187.200.000
48.859.200
59.342.400
33.939.360
63.905.400
71.042.400
58.593.600
56.628.000
46.074.600
17.570.358
43.865.640
138.827.520
70.763.472
63.147.240
192.816.000
50.324.976
61.122.672
34.957.541
65.822.562
73.173.672
60.351.408
58.326.840
47.456.838
18.862.875
47.092.500
149.040.000
75.969.000
67.792.500
207.000.000
54.027.000
65.619.000
37.529.100
70.664.625
78.556.500
64.791.000
62.617.500
50.947.875
17.678.250
44.135.000
139.680.000
71.198.000
63.535.000
194.000.000
50.634.000
61.498.000
34.084.400
64.178.500
71.346.000
58.844.000
58.685.000
47.748.250
18.407.250
45.955.000
145.440.000
74.134.000
66.155.000
202.000.000
52.722.000
64.034.000
38.435.600
72.371.500
76.659.000
63.226.000
61.105.000
49.717.250
18.589.500
46.410.000
147.024.000
74.941.400
66.875.500
204.200.000
53.296.200
64.731.400
35.353.500
66.568.125
77.493.900
63.914.600
61.770.500
50.258.725
Student 9
Student 10
Student 11
Student 12
Student 13
Student 14
Student 15
Claims 9
Claims 10
Claims 11
Claims 12
Claims 13
Claims 14
Claims 15
69.515.200
74.426.600 71.706.440
78.733.520
70.860.168
73.694.575
75.905.412
61.134.000
65.453.250 63.061.050
69.240.900
62.316.810
64.809.482
66.753.767
Est. 162,957,398
Est. 162,957,399
Est. 162,957,400Est. 162,957,401Est. 162,957,402 Est. 162,957,403Est. 162,957,404
72.371.800
77.485.025 74.653.085
81.968.930
73.772.037
76.722.918
79.024.606
62.100.000
66.487.500 64.057.500
70.335.000
63.301.500
65.833.560
67.808.567
51.759.200
55.416.100 53.390.740
58.622.920
52.760.628
54.871.053
56.517.185
57.293.000
61.340.875 59.098.975
64.890.550
58.401.495
60.737.555
62.559.681
79.948.000
85.596.500 82.468.100
90.549.800
81.494.820
84.754.613
87.297.251
64.032.000
68.556.000 66.050.400
72.523.200
65.270.880
67.881.715
69.918.167
41.400.000
44.325.000 42.705.000
46.890.000
42.201.000
43.889.040
45.205.711
50.784.000
56.193.600 52.384.800
57.518.400
51.766.560
53.837.222
55.452.339
60.959.200
67.452.680 62.880.740
69.042.920
62.138.628
64.624.173
66.562.898
61.893.000
68.485.950 63.843.975
70.100.550
63.090.495
65.614.115
67.582.538
52.348.000
57.924.200 53.998.100
59.289.800
53.360.820
55.495.253
57.160.110
64.013.600
70.832.440 71.667.400
72.502.360
65.252.124
67.862.209
69.898.075
31.280.000
34.612.000 35.020.000
35.428.000
31.885.200
33.160.608
34.155.426
56.543.200
62.566.280 63.303.800
64.041.320
57.637.188
59.942.676
61.740.956
41.243.600
45.636.940 46.174.900
46.712.860
42.041.574
43.723.237
45.034.934
72.496.000
80.218.400 81.164.000
82.109.600
73.898.640
76.854.586
79.160.223
65.918.000
72.939.700 73.799.500
74.659.300
67.193.370
69.881.105
71.977.538
74.842.000
82.814.300 83.790.500
84.766.700
76.290.030
79.341.631
81.721.880
42.062.400
46.542.960 47.091.600
47.640.240
42.876.216
44.591.265
45.929.003
33.359.200
36.912.680 37.347.800
37.782.920
34.004.628
35.364.813
36.425.758
71.688.750
69.503.950 70.323.250
71.142.550
64.028.295
66.589.427
68.587.110
80.745.000
78.284.200 79.207.000
80.129.800
72.116.820
75.001.493
77.251.538
73.080.000
70.852.800 71.688.000
72.523.200
65.270.880
67.881.715
69.918.167
58.338.000
56.560.080 57.226.800
56.426.736
50.784.062
52.815.425
54.399.888
59.272.500
57.466.100 58.143.500
57.330.620
51.597.558
53.661.460
55.271.304
27.940.500
27.088.980 27.408.300
27.025.116
24.322.604
25.295.509
26.054.374
35.406.000
34.326.960 34.731.600
34.246.032
30.821.429
32.054.286
33.015.915
43.407.000
40.719.900 42.580.200
41.984.904
37.786.414
39.297.870
40.476.806
45.680.250
42.852.425 44.810.150
44.183.678
39.765.310
41.355.923
42.596.600
73.710.000
69.147.000 72.306.000
71.295.120
64.165.608
66.732.232
68.734.199
78.960.000
74.072.000 77.456.000
76.373.120
68.735.808
71.485.240
73.629.798
55.650.000
52.205.000 54.590.000
53.826.800
48.444.120
50.381.885
51.893.341
Est. 65,750,008Est. 65,750,009Est. 65,750,010 Est. 65,750,011 Est. 65,750,012 Est. 65,750,013 Est. 65,750,014
Est. 46,400,008Est. 46,400,009Est. 46,400,010 Est. 46,400,011 Est. 46,400,012 Est. 46,400,013 Est. 46,400,014
71.925.000
67.472.500 70.555.000
69.568.600
62.611.740
65.116.210
67.069.696
61.136.250
57.351.625 59.971.750
59.133.310
53.219.979
55.348.778
57.009.242
92.820.000
87.074.000 91.052.000
89.779.040
80.801.136
84.033.181
86.554.177
69.825.000
65.502.500 68.495.000
67.537.400
60.783.660
63.215.006
65.111.457
63.236.250
59.321.625 62.031.750
61.164.510
55.048.059
57.249.981
58.967.481
24.360.000
22.852.000 23.896.000
23.561.920
21.205.728
22.053.957
22.715.576
39.270.000
36.839.000 38.522.000
37.983.440
34.185.096
35.552.500
36.619.075
30.975.000
29.057.500 30.385.000
29.960.200
26.964.180
28.042.747
28.884.030
19.136.250
47.775.000
151.200.000
77.070.000
68.775.000
210.000.000
54.810.000
66.570.000
33.359.200
71.688.750
79.695.000
65.730.000
63.525.000
51.686.250
17.951.625 18.771.750
44.817.500 46.865.000
141.840.000 148.320.000
72.299.000 75.602.000
64.517.500 67.465.000
197.000.000 206.000.000
51.417.000 53.766.000
62.449.000 65.302.000
36.912.680 37.347.800
69.503.950 70.323.250
77.266.200 78.177.000
63.726.800 64.478.000
59.592.500 62.315.000
48.486.625 50.701.750
18.509.310
46.209.800
146.246.400
74.545.040
66.521.800
203.120.000
53.014.320
64.389.040
37.782.920
71.142.550
79.087.800
65.229.200
61.443.800
49.992.910
16.658.379
41.588.820
131.621.760
67.090.536
59.869.620
182.808.000
47.712.888
57.950.136
34.004.628
64.028.295
71.179.020
58.706.280
55.299.420
44.993.619
17.324.714
43.252.373
136.886.630
69.774.157
62.264.405
190.120.320
49.621.404
60.268.141
35.364.813
66.589.427
74.026.181
61.054.531
57.511.397
46.793.364
17.844.456
44.549.944
140.993.229
71.867.382
64.132.337
195.823.930
51.110.046
62.076.186
36.425.758
68.587.110
76.246.966
62.886.167
59.236.739
48.197.165
Student 16
Student 17
Student 18
Student 19
Student 20
Student 21
Claims 16
Claims 17
Claims 18
Claims 19
Claims 20
Claims 21
82.670.196
74.009.509
74.796.844
76.765.182
74.718.110
71.852.210
72.702.945
65.086.446
65.778.855
67.509.878
65.709.614
63.189.245
Est. 162,957,405Est. 162,957,406Est. 162,957,407
Est. 162,957,408 Est. 162,957,408Est. 162,957,397
86.067.377
77.050.794
77.870.484
79.919.707
77.788.515
74.804.846
73.851.750
66.114.900
66.818.250
68.576.625
66.747.915
64.187.721
61.554.066
55.105.545
55.691.774
57.157.347
55.633.151
53.499.277
68.135.078
60.997.117
61.646.023
63.268.286
61.581.132
59.219.116
95.077.290
85.116.812
86.022.310
88.286.055
85.931.760
82.635.747
76.149.360
68.171.808
68.897.040
70.710.120
68.824.517
66.184.672
49.234.500
44.076.600
44.545.500
45.717.750
44.498.610
42.791.814
60.394.320
54.067.296
54.642.480
56.080.440
54.584.962
52.491.292
72.495.066
64.900.345
73.185.495
67.316.847
65.521.731
63.008.569
73.605.578
65.894.517
74.306.583
68.348.036
66.525.422
63.973.762
62.254.290
55.732.412
62.847.188
57.807.555
56.266.020
54.107.871
76.127.478
68.152.218
76.852.502
70.689.801
74.677.431
66.165.654
37.199.400
33.302.320
37.553.680
34.542.300
36.490.840
32.331.593
67.243.386
60.198.841
67.883.799
62.440.287
65.962.560
58.444.109
49.048.503
43.910.088
49.515.632
45.545.039
48.114.246
42.630.156
86.215.080
77.183.024
87.036.176
80.056.860
84.572.888
74.933.221
78.392.265
70.179.742
79.138.858
72.792.818
76.899.079
68.134.077
89.005.035
79.680.698
89.852.702
82.647.533
87.309.701
77.358.090
50.022.252
44.781.826
50.498.654
46.449.234
49.069.447
43.476.483
39.105.322
35.515.945
40.049.895
36.838.347
38.916.408
34.480.693
73.632.539
66.873.997
75.411.103
69.363.986
73.276.827
64.924.691
82.934.343
75.322.012
80.931.098
81.812.526
82.533.694
76.576.524
75.061.512
68.171.808
73.248.432
74.046.187
74.698.896
69.307.231
58.401.672
54.733.934
56.991.003
57.611.697
58.119.538
53.924.549
59.337.192
55.610.701
57.903.926
58.534.563
59.050.539
54.788.351
27.970.995
26.214.363
27.295.367
27.592.643
27.835.869
25.826.714
35.444.643
33.218.651
34.588.492
34.965.199
35.273.413
32.727.426
43.454.376
40.725.357
42.404.753
42.866.587
43.244.451
40.123.125
45.730.107
42.858.168
44.625.515
45.111.535
45.509.188
42.224.397
73.790.449
69.156.266
72.008.071
72.792.318
73.433.974
68.133.609
79.046.179
74.081.926
77.136.851
77.976.956
78.664.314
72.986.430
55.710.738
52.211.996
54.365.068
54.957.163
55.441.604
51.439.904
Est. 65,750,015 Est. 65,750,016 Est. 65,750,017Est. 65,750,018 Est. 65,750,018 Est. 65,750,007
Est. 46,400,015 Est. 46,400,016 Est. 46,400,017Est. 46,400,018 Est. 46,400,018 Est. 46,400,007
72.003.501
67.481.542
70.264.286
71.029.541
71.655.658
66.483.650
61.202.976
57.359.311
59.724.643
60.315.976
60.907.309
56.455.754
92.921.306
87.085.669
90.676.830
91.574.621
92.472.411
85.713.845
69.901.209
65.511.278
68.212.774
68.888.148
69.563.522
64.479.307
63.305.268
59.329.575
61.776.155
62.387.800
62.999.445
58.394.981
24.386.587
22.855.062
23.797.539
24.033.158
24.268.778
22.495.036
39.312.860
36.843.937
38.363.274
38.743.109
39.122.943
36.263.550
31.008.807
29.061.394
30.259.802
30.559.404
30.859.006
28.603.602
19.157.136
47.827.143
151.365.024
77.154.116
68.850.063
210.229.200
54.869.821
66.642.656
39.105.322
73.632.539
81.855.873
67.512.222
63.594.333
51.742.662
17.954.031
44.823.506
141.859.008
72.308.689
64.526.146
197.026.400
51.423.890
62.457.369
35.515.945
66.873.997
74.342.532
61.315.448
59.600.486
48.493.123
18.694.403
46.671.898
147.708.864
75.290.490
67.187.018
205.151.200
53.544.463
65.032.930
40.049.895
75.411.103
79.878.678
65.881.492
62.058.238
50.492.839
18.879.496
47.133.996
149.317.574
76.110.486
67.918.758
207.385.520
54.127.621
65.741.210
36.838.347
69.363.986
80.748.644
66.599.013
62.734.120
51.042.761
19.064.589
47.596.094
150.633.792
76.781.391
68.517.454
209.213.600
54.604.750
66.320.711
38.916.408
73.276.827
81.460.434
67.186.076
63.287.114
51.492.697
17.671.208
44.117.420
139.761.250
71.239.415
63.571.957
194.112.847
50.663.453
61.533.772
34.480.693
64.924.691
75.580.731
62.336.676
58.719.136
47.776.024
Student 22
Student 23
Student 24
Student 25
Student 26
Student 27
Claims 22
Claims 23
Claims 24
Claims 25
Claims 26
Claims 27
67.799.009
72.589.156
69.936.151
76.789.747
79.093.439
86.142.344
59.624.724
63.837.340
61.504.199
67.531.481
69.557.425
75.756.469
Est. 162,957,398Est. 162,957,399Est. 162,957,400 Est. 162,957,401Est. 162,957,402
Est. 162,957,403
70.585.085
75.572.075
72.810.050
79.945.281
82.343.639
89.682.206
60.566.875
64.846.057
62.476.048
68.598.570
70.656.527
76.953.524
50.481.369
54.047.987
52.072.629
57.175.637
58.890.906
64.139.337
55.878.550
59.826.491
57.639.940
63.288.532
65.187.188
70.996.751
77.974.244
83.483.294
80.432.128
88.314.307
90.963.736
99.070.536
62.451.178
66.863.489
64.419.748
70.732.747
72.854.730
79.347.633
40.377.917
43.230.704
41.650.699
45.732.380
47.104.351
51.302.349
49.530.245
54.806.292
51.091.524
56.098.386
57.781.337
62.930.881
59.454.239
65.787.408
61.328.340
67.338.388
69.358.540
75.539.859
60.364.986
66.795.169
62.267.795
68.369.908
70.421.005
76.697.012
51.055.633
56.494.167
52.664.995
57.826.053
59.560.835
64.868.970
62.433.232
69.083.729
69.898.075
70.712.422
72.833.794
79.324.832
30.507.759
33.757.499
34.155.426
34.553.354
35.589.954
38.761.775
55.147.261
61.021.644
61.740.956
62.460.268
64.334.076
70.067.608
40.225.378
44.510.255
45.034.934
45.559.613
46.926.401
51.108.540
70.706.219
78.237.968
79.160.223
80.082.478
82.484.953
89.836.113
64.290.616
71.138.965
71.977.538
72.816.111
75.000.595
81.684.740
72.994.301
80.769.781
81.721.880
82.673.980
85.154.199
92.743.246
41.023.963
45.393.907
45.929.003
46.464.098
47.858.021
52.123.187
32.535.628
36.001.380
36.425.758
36.850.135
37.955.639
40.747.746
69.918.898
67.788.036
68.587.110
69.386.183
71.467.768
76.725.106
78.751.567
76.351.520
77.251.538
78.151.555
80.496.102
86.417.585
71.275.801
69.103.586
69.918.167
70.732.747
72.854.730
78.214.096
55.456.196
53.766.103
54.399.888
53.639.346
55.248.526
59.312.738
56.344.533
54.627.367
55.271.304
54.498.579
56.133.536
60.262.852
26.560.284
25.750.828
26.054.374
25.690.119
26.460.822
28.407.343
33.657.000
32.631.263
33.015.915
32.554.333
33.530.963
35.997.580
41.262.764
38.708.402
40.476.806
39.910.917
41.108.244
44.132.264
43.423.719
40.735.584
42.596.600
42.001.075
43.261.107
46.443.496
70.068.844
65.731.249
68.734.199
67.773.255
69.806.453
74.941.580
75.059.502
70.412.962
73.629.798
72.600.410
74.778.422
80.279.300
52.900.979
49.626.157
51.893.341
51.167.842
52.702.877
56.579.826
Est. 65,750,008 Est. 65,750,009 Est. 65,750,010 Est. 65,750,011 Est. 65,750,012Est. 65,750,013
Est. 46,400,008 Est. 46,400,009 Est. 46,400,010 Est. 46,400,011 Est. 46,400,012Est. 46,400,013
68.372.020
64.139.466
67.069.696
66.132.022
68.115.983
73.126.756
58.116.217
54.518.546
57.009.242
56.212.219
57.898.586
62.157.742
88.234.841
82.772.684
86.554.177
85.344.099
87.904.422
94.370.879
66.375.757
62.266.781
65.111.457
64.201.160
66.127.195
70.991.668
60.112.480
56.391.232
58.967.481
58.143.081
59.887.374
64.292.830
23.156.655
21.723.148
22.715.576
22.397.999
23.069.939
24.767.018
37.330.125
35.019.212
36.619.075
36.107.119
37.190.332
39.926.141
29.444.885
27.622.106
28.884.030
28.480.214
29.334.620
31.492.544
18.190.950
45.414.991
143.730.962
73.262.865
65.377.625
199.626.336
52.102.474
63.281.549
32.535.628
69.918.898
77.727.490
64.107.258
60.386.967
49.133.032
17.064.843
42.603.587
134.833.331
68.727.545
61.330.439
187.268.515
48.877.082
59.364.119
36.001.380
67.788.036
75.358.652
62.153.513
56.648.726
46.091.463
17.844.456
44.549.944
140.993.229
71.867.382
64.132.337
195.823.930
51.110.046
62.076.186
36.425.758
68.587.110
76.246.966
62.886.167
59.236.739
48.197.165
17.594.980
43.927.110
139.022.062
70.862.634
63.235.730
193.086.197
50.395.497
61.208.324
36.850.135
69.386.183
77.135.280
63.618.822
58.408.575
47.523.340
18.122.829
19.455.987
45.244.923
48.573.246
143.192.724 153.726.318
72.988.513
78.357.721
65.132.801
69.924.124
198.878.783 213.508.776
51.907.362
55.725.790
63.044.574
67.682.282
37.955.639
40.747.746
71.467.768
76.725.106
79.449.339
85.293.820
65.527.386
70.347.735
60.160.832
64.586.405
48.949.040
52.549.847
Student 28
Student 29
Student 30
Student 31
Student 32
Claims 28
Claims 29
Claims 30
Claims 31
Claims 32
77.117.908
77.938.311
79.989.320
77.856.271
74.870.003
67.820.077
68.541.567
70.345.292
68.469.418
65.843.194
Est. 162,957,404Est. 162,957,405Est. 162,957,406Est. 162,957,407 Est. 162,957,407
80.286.928
81.141.044
83.276.334
81.055.632
77.946.649
68.891.726
69.624.617
71.456.843
69.551.327
66.883.605
57.419.978
58.030.829
59.557.956
57.969.743
55.746.246
63.558.996
64.235.155
65.925.554
64.167.539
61.706.319
88.691.718
89.635.247
91.994.069
89.540.894
86.106.449
71.035.024
71.790.716
73.679.945
71.715.147
68.964.429
45.927.817
46.416.411
47.637.896
46.367.552
44.589.070
56.338.122
56.937.464
58.435.818
56.877.530
54.695.926
67.626.159
76.259.286
70.144.155
68.273.644
65.654.929
68.662.087
77.427.459
71.218.654
69.319.490
66.660.660
58.073.173
65.486.770
60.235.472
58.629.193
56.380.402
71.014.612
80.080.307
73.658.773
77.813.883
68.944.611
34.701.017
39.130.935
35.993.077
38.023.455
62.727.192
70.734.919
65.062.779
68.732.987
45.754.312
51.595.288
47.457.930
50.135.044
80.424.711
90.691.695
83.419.248
88.124.949
73.127.291
82.462.690
75.850.116
80.128.840
83.027.287
93.626.515
86.118.729
90.976.708
46.662.662
52.619.598
48.400.102
51.130.364
37.007.614
41.731.991
38.385.558
40.550.897
69.682.705
78.578.369
72.277.274
76.354.453
78.485.537
84.330.204
85.248.652
86.000.109
71.035.024
76.324.866
77.156.127
77.836.250
55.587.783
57.880.063
58.510.440
59.026.203
56.478.228
58.807.227
59.447.702
59.971.727
26.623.307
27.721.175
28.023.089
28.270.109
33.736.862
35.128.073
35.510.656
35.823.678
41.360.672
43.066.267
43.535.306
43.919.065
43.526.755
45.321.673
45.815.275
46.219.132
70.235.104
73.131.397
73.927.878
74.579.544
75.237.604
78.340.186
79.193.396
79.891.477
53.026.503
55.213.163
55.814.495
56.306.493
Est. 65,750,014 Est. 65,750,015 Est. 65,750,016 Est. 65,750,017
Est. 46,400,014 Est. 46,400,015 Est. 46,400,016 Est. 46,400,017
68.534.254
71.360.409
72.137.601
72.773.486
58.254.116
60.656.348
61.256.905
61.857.463
88.444.205
92.091.389
93.003.185
93.914.981
66.533.254
69.276.893
69.962.803
70.648.713
60.255.116
62.739.863
63.361.050
63.982.237
23.211.601
24.168.781
24.408.076
24.647.371
37.418.702
38.961.741
39.347.501
39.733.261
29.514.752
30.731.855
31.036.131
31.340.406
33.689.520
60.898.761
44.420.623
78.080.416
70.995.708
80.607.130
45.302.495
35.928.882
67.651.528
79.792.738
72.218.135
54.765.772
55.643.049
26.229.611
33.237.974
40.749.046
42.883.098
69.196.494
74.125.019
52.242.367
Est. 65,750,017
Est. 46,400,017
67.520.795
57.336.463
87.050.981
65.485.184
59.305.943
22.845.959
36.829.261
29.049.818
18.234.114
45.522.753
144.072.009
73.436.704
65.532.754
200.100.012
52.226.103
63.431.704
37.007.614
69.682.705
77.464.918
63.890.697
60.530.254
49.249.615
18.986.036
47.399.980
150.013.122
76.465.022
68.235.135
208.351.559
54.379.757
66.047.444
41.731.991
78.578.369
83.233.582
68.648.515
63.026.347
51.280.527
19.174.016
47.869.286
151.646.929
77.297.809
68.978.290
210.620.734
54.972.012
66.766.773
38.385.558
72.277.274
84.140.087
69.396.172
63.712.772
51.839.028
19.361.997
48.338.593
152.983.679
77.979.181
69.586.326
212.477.332
55.456.584
67.355.314
40.550.897
76.354.453
84.881.772
70.007.891
64.274.393
52.295.983
17.946.879
44.805.652
141.941.525
72.350.750
64.563.680
197.141.007
51.453.803
62.493.699
35.928.882
67.651.528
78.755.121
64.954.817
59.635.155
48.521.330
Year
Per Risk XL treaty Unadjusted Losses
2011
Panasonic Corporation – Tsunami
Nissan Japan – Tsunami
Fukushima pollution liability – Tsunami
Toyota Corporation – Tsunami
Super Dry Corporation – Tsunami
Sky New Zealand – Earthquake
Next New Zealand – Earthquake
Macys New Zealand – Earthquake
Christ Church Council NZ – Earthquake
House damage – NZ – Earthquake
Sony Thailand Floods
Dell Thailand Floods
Daimler Thailand – floods
Thai Hotel – Floods
Thai Resorts – floods
2011
2012
2013
2014
2015
2016
2017
2018
2019
Incurred loss &
LAE
74.718.110
65.709.614
162.957.408
77.788.515
66.747.915
55.633.151
61.581.132
85.931.760
68.824.517
44.498.610
54.584.962
65.521.731
66.525.422
56.266.020
74.677.431
2019
2020
2021
Retention
50.000.000
50.000.000
112.957.408
50.000.000
50.000.000
50.000.000
50.000.000
50.000.000
50.000.000
44.498.610
50.000.000
50.000.000
50.000.000
50.000.000
50.000.000
250.000.000
Excess over
£50,000,000 Pure
BC
24.718.110
15.709.614
25.000.000
25.000.000
16.747.915
5.633.151
11.581.132
25.000.000
18.824.517
0
4.584.962
15.521.731
16.525.422
6.266.020
24.677.431
Subtotals
168.214.439
67.575.566
Excess over
£75,000,000 Pure
BC
0
0
25.000.000
2.788.515
0
0
0
10.931.760
0
0
0
0
0
0
0
Subtotals
35.931.760
0
Spill Over Per Risk Adjuste
1st Layer
62.957.408

#NAME?
#NAME?
Per Risk
Adjusted 2nd
Layer QS R (60%)
#NAME?
#NAME?
32.750.977
39.313.039
39.915.253
33.759.612
44.806.458
Subtotal for
Retention
190.545.339
257.575.566
QS Rein (40%)
21.833.985
26.208.692
26.610.169
22.506.408
29.870.972
Subtotal for QS
Reins
Spill over
127.030.226
60.000.000
67.030.226
Per PERIL
Catastrophe Excess of Loss Treaty – computations
[100m]
50m
CAT XL Losses
Retention
Layer 1
Total:
JAPAN
Total:
New Zealand

244.498.610
144.498.610

50.000.000
Cat XL
Adjusted
1st Layer
mputations
50m
Layer 2
Per Risk
Adjusted
2nd Layer
>200m
Spill Over

50.000.000

=T5*relativity =U5*relativity
44.498.610 =T10*relativity=U10*relativity
Glasgow Caledonian University
MSc Insurance and Sustainable Risk Management
Module: Reinsurance, Risk Financing and Securitisation of Insurance Risks
Coursework 2 topics: Reinsurance Programme Design and Risk Securitisation Issues
THIS COURSEWORK CONSISTS OF 70% OF OVERALL EXAMINABLE COMPONENT
Analytical Report
You work for The Stan Reinsurance Company (hereinafter referred as Stan Re), located in
Bermuda. Your company has received an inward reinsurance business proposal from a UKbased primary insurer named Limestreet Insurance Company (hereinafter referred to as
Limestreet). The Limestreet requires Stan Re to be the lead underwriter of its Property, Liability
and Accident businesses.
A summary of the Treaty Slips for (1) per risk Excess of Loss; and (2) catastrophe Excess of
Loss including the relevant information necessary to carry out the assessment are available
below.
1) Per Risk Excess of Loss Treaty Summary
Ceding
Company
Agreement
Limestreet Insurance Company Ltd
Period
12 months commencing 1st of January 2022. Losses occurring
irrespective of attachment dates of original policies.
Type
Excess of Loss cover
Class
Property, Liability and Accident businesses
Territory
Worldwide
This agreement between the ceding company and the reinsurer
consists of two parts being the specific conditions specified in the
treaty summary including any appendix and the general terms and
conditions.
1st Layer: To pay US$ 25,000,000 ultimate net loss each and every risk
in excess of US$ 50,000,000 ultimate net loss each and every risk.
2nd Layer: To pay US$ 25,000,000 ultimate net loss each and every
risk in excess of US$ 75,000,000 ultimate net loss each and every risk.
Reinstatements 1st layer: four free
2nd layer: one free
Premium and
As a part of this coursework, you are required to calculate the Minimum
rates
Deposit Premium [see question (b) below].
Brokerage
The advisable brokerage commission is 10% (0% on reinstatements).
However, it is expected that students should use another rate based on
their judgement on the basis of practical circumstances.
General
See Questions (a) and (c) below.
conditions
Data
Supplied in Tables 1, 2, 3, 4 and 5 below
Limits and
Deductibles
1
Table 1: GNPI
Fiscal Year
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
GNPI (estimated) in US$
900,000,000
750,000,000
690,455,000
610,500,000
500,100,000
480,000,000
404,400,000
366,500,000
310,300,000
255,800,000
247,200,000
238,000,000
Table 2: Projected Income for 2022
Country/region
North America
Projected Income (in US$)
205,000,000
Europe
250,250,000
Japan
102,000,000
Asia
170,250,000
Middle East
161,100,000
South America
100,000,000
Australasia
110,150,000
Caribbean
60,300,000
Africa
40,950,000
Total
2
1,200,000,000
Table 3: Risk Profile by Sum Insured [All policies in force on 31 December 2021]
Sum Insured in US$ 000
Number of Risks
0 – 10,000
10,000-20,000
20,000 – 30,000
30,000 – 40,000
40,000 – 50,000
50,000 – 60,000
60,000 – 70,000
70,000 – 80,000
80,000 – 90,000
0ver 90,000
1,300
1040
850
300
210
150
100
72
50
120
4,192
Total
Premium in US$
million
250
200
120
130
110
150
145
100
90
165
1460
2) Catastrophe Excess of Loss Treaty Summary
SLIP DETAILS
CEDING COMPANY
Limestreet Insurance Company Ltd
AGREEMENT FORMAT This agreement between the ceding company and the reinsurer consist
of two parts being the specific conditions specified in the treaty
summary including any appendix, and the General Terms and
conditions specified in the attached document.
12 months commencing 1 January 2022. Losses occurring irrespective
PERIOD
of attachment dates of original policies.
TYPE
Catastrophe Excess of Loss Cover
CLASS
1) The reinsured’s net retained account of direct insurance and
facultative reinsurances in respect of
a) Home and overseas business written in overseas fire
department
b) Its participation in the business of international oil insurers
written in its fire department
2) Fire and allied perils written in the home personal department in
respect of the reinsurer’s householders comprehensive and private
house policies including small craft and caravans
Worldwide, excluding risks situated in the USA
TERRITORY
EXCLUSIONS
Note:
As a part of your answer, you are required to advise on the
exclusions to include and create the schedule
3
LIMIT AND
DEDUCTIBLES
1st Layer
To pay US$50,000,000 Ultimate Net Loss each and every loss
occurrence IN EXCESS OF US$100,000,000 Ultimate Net Loss each
and every loss occurrence
GROWTH OF LINE
LIMITS
2nd Layer
To pay US$50,000,000 Ultimate Net Loss each and every loss
occurrence IN EXCESS OF US$150,000,000 Ultimate Net Loss each
and every loss occurrence
Note: Line limits have gone up at equal intervals 50% in the past five
years
WARRANTY
Two Risk warranty.
REINSTATEMENT
Applicable to both layers.
One full reinstatement at 100% additional premium as to time, pro-rata
as to amount reinstated only.
RATES
1st layer – Adjustable Rate: 2.25% of GNPI
2nd Layer Adjustable Rate: 1.10% of GNPI
PREMIUM
DEPOSIT PREMIUMS
Minimum and deposit premium (please calculate), payable in halfyearly in advance.
DEDUCTIONS
PREMIUM ADJUSTMENT BASIS
Both layers:
Average net retained aggregate sums insured for earthquake,
windstorm for the 12 months period commencing January 1, 2022.
Brokerage 10% (0% on reinstatement)
Note: This brokerage rate is for general guidelines only. However,
it is expected that students should use the brokerage rate based
on market reality and circumstances.
GENERAL
CONDITIONS
Not supplied [students need to decide]
Note: It is expected that the students should advise on the
general conditions based on market reality and circumstances
Table 4: Big Losses – Home and Foreign Account
Note: Although Tables 1, 2, 3 and 5 are the same for all students, Table 4 is different
and allocated separately to each student. You are required to use the allocated data in
your analysis.
Table 5: Inflation rates
2011 2012
2013
2014
2015
2016
2.6% 1.9%
3%
1.5% 3.2% 2.5%
The average Future Annual Inflation is 3.5%.
Table 6: Loss Development Factors
4
2017
2.2%
2018
2.6%
2019
3.2%
2020
4.25%
2021
4.5%
Year
1 to 2 2 to 3 3 to 4 4 to 5 5 to 6 6 to 7 7 to 8 8 to 9 9 to 10
Loss
1.9
1.5
1.3
1.25
1.15
1.1
1.08
1.02
1.01
Development
Factor
Note that the Discount Rate is 5%, Ultimate Development of the Loss for the next five years
is 1.24 (10 to ultimate).
REQUIRED:
In considering the above information, you are required to produce an analytical report that
helps your manager to (a) underwrite, (b) price, and (c) redesign the reinsurance programme
to make the treaties more effective to manage Limestreet’s risk exposures.
In the report you should address the following issues:
a) An analysis (pricing of the layers to the per risk excess of loss – determine an adjustable
Minimum Deposit Premium and Catastrophe excess of loss) and assessment of the
appropriateness and acceptability of the terms of this business proposition. (Assume the
average delay in claim settlement for the liability claims is about three years).
b) Given that the nature of the per risk excess of loss book has no territorial limit, suggest
and justify the rationale behind the contractual conditions that you would like to put in place
to make this business less risky and acceptable.
c) Given that the chance of exhausting the catastrophe cover is high:
i.
Evaluation and price an alternative top and drop cover for catastrophe losses up
to a coverage amount of US$50,000,000 (size of the top and drop layer);
ii.
Explore how you can use a collateralised insurance-linked security in one of the
territories to bridge the gap for the spillover layer that will give catastrophe cover
of up to a limit of US$500 million.
d) An assessment of how implementing a 40% quota share with a limit US$100 million
instead of the per risk excess of loss, alongside the catastrophe excess of loss structure
similar to the one above will impact the price and terms of the Catastrophe excess of loss
treaty. (Assume that there is a per-event accumulation limit of US$60 million on the Quota
Share and that all the losses are incurred at 100%).
e) Also, discuss how you can control the impact of inflation on the treaty pricing arising from
liability claims.
f) Given the nature of the book, critically evaluate why it might be beneficial to arrange the
excess of loss treaties by region or introduce a buffer excess of loss for certain problematic
perils. In your answer provide historical statistical evidence on the main drivers of regional
claims.
g) The Fukushima employers’ liability loss has been outstanding since 2011 and was revised
upwards from an initial claim of US$25 million. Using the loss development factors above
evaluate an alternative risk financing instrument you would use to transfer the risk and
determine the price which your company would pay for the transferred portfolio.
5
Allocation of Marks
Question No.
a
b
c
d
e
f
g
Total
Marks
20
10
20
10
10
10
20
100
The detailed assessment criteria are added on the table at pages 8and 9 of this document.
Further information is available on Module Handbook.
PLEASE NOTE:
SUBMISSION DEADLINE AND LINK:
The students (both on-campus and distance learning) must submit this electronic version of
the coursework (Word Version of the Report) via “Turnitin” on GCU-Learn using the
appropriate link and the associated EXCEL worksheets (if necessary) by email to the module
tutor on or before Tuesday, 10 May 2022 at 18:00 BST. Before final submission, you may use
the trial submission link available on GCU Learn to check the similarity index of your report
(word Version Only).
PLAGIARISM: Please refer to the University Guidelines on plagiarism. You are advised to
consider this issue very seriously.
WORD COUNT: 3,000 (+/- 10%). This excludes references and appendices.
Any coursework not submitted by the due date will be zero marked unless an approved MITS
is submitted for consideration by the Assessment Board.
6
GLOSSARY OF KEY WORDS
Analyse
Find the relevant facts and examine these in depth. Examine the relationship between
various facts and make conclusions or recommendations.
Asses
To judge or decide the amount, value, quality, or importance of something
Construct
To build or make something; construct a table.
Critically analyse
The analysis of information by comparing and contrasting their strength and weakness
through arguments and counterarguments.
Describe
Give an account in words (someone or something) including all relevant characteristics,
qualities or events.
Devise
To plan or create a method, procedure or system.
Discuss
To consider something in detail; examining the different ideas and opinions about
something, for example to weigh up alternative views.
Explain
To make something clear and easy to understand with reasoning and/or justification.
Identify
Recognise and name.
Justify
Support an argument or conclusion. Prove or show grounds for a decision.
Outline
Give a general description briefly showing the essential features.
Recommend with reasons
Provide reasons in favour.
State
Express main points in brief, clear form.
7
ASSESSMENT CRITERIA
CRITERION
70% & More
60-69%
50-59%
FAIL – 49% or Less
1
Presentation of
assignment
Carefully and logically
organised
Shows organisation and
coherence
Disorganised/
incoherent
2
Clarity of
expression
including accuracy,
spelling, grammar,
punctuation
Communication
and presentation
Shows a polished and
imaginative approach to the
topic
Fluent writing style appropriate
to document. Grammar and
spelling accurate.
Language fluent
Grammar and spelling
accurate
Language mainly fluent
Grammar and spelling
mainly accurate
Can engage effectively in debate
in a professional manner and
produce detailed and coherent
project reports
Can communicate
effectively and report
practical procedures in
a clear and concise
manner with all relevant
information in a variety
of formats
Meaning unclear
and/or grammar
and/or spelling
contain frequent
errors
Communication is
unstructured and
unfocused and/or in
a format
inappropriate to the
discipline
3
4
Logical Structure
5
Presentation
6
Conforming with
instructions (e.g.
word length)
Clear, imaginative, logical
structure
Material is imaginatively
presented resulting in clarity of
message and information
Can communicate
effectively in a format
appropriate to the
discipline and report
procedures in a clear
and concise manner
with all relevant
information
Clear, basic, logical structure
Material is carefully
structured with clear
message and visual
effect
Material included is
relevant to topic and
has been structured.
Visual aspect of
presentation is limited
Work has been submitted within time boundaries and within prescribed parameters
8
Structure is not
logical
Not all material is
relevant and/or is
presented in a
disorganised manner
Work has been
submitted late or
deviates significantly
from parameters
7
Attention to
purpose
8
Question
understanding
9
Content and range
Has addressed the purpose of
the assignment comprehensively
and
imaginatively
Has addressed the
purpose of the
assignment coherently
and with some attempt
to demonstrate
imagination
Answer comprehensively addresses the key components of
the question
Has addressed the
main purpose of the
assignment
Fails to address the
task set
Answer consistently
addresses the key
components of the
question
Comprehensive/detailed
knowledge of key issues
Reasonable knowledge
of key issues
Has given a factual
and/or conceptual
knowledge base and
appropriate terminology
10 Critical reasoning
Consistently demonstrates
application of critical analysis
well integrated in the text
11 Use of literature/
evidence of reading
Has developed and justified
using own ideas based on a
wide range of sources which
have been thoroughly analysed,
applied and discussed
Demonstrates
application of theory
through critical analysis
of the topic area
Literature is presented
uncritically, in a purely
descriptive way and
indicates limitations of
understanding
12 Referencing
Referencing is consistently
accurate
Clear application of
theory through critical
analysis/critical thought
of the topic area
Able to critically
appraise the literature
and theory gained from
variety of sources,
developing own ideas in
the process
Referencing is mainly
accurate
Answer does not
consistently
addresses the key
components of the
question
Lacks evidence of
knowledge relevant
to the key issues
and/or significantly
misuses terminology
Lacks critical thought
/analysis / reference
to theory
END
9
Some attempt at
referencing
Either no evidence of
literature being
consulted or
irrelevant to the
assignment set
Referencing is
absent/
unsystematic
Basics of Reinsurance Pricing
Actuarial Study Note
David R. Clark, FCAS
First Version 1996
Revised 2014
Basics of Reinsurance Pricing
Introduction
Like primary insurance, reinsurance is a mechanism for spreading risk. A reinsurer
takes some portion of the risk assumed by the primary insurer (or other reinsurer) for
premium charged. Most of the basic concepts for pricing this assumption of risk are the
same as those underlying ratemaking for other types of insurance. This study note will
assume a knowledge of basic ratemaking concepts on the part of the reader.
A major difference between reinsurance and primary insurance is that a reinsurance
program is generally tailored more closely to the buyer; there is no such thing as the
“average” reinsured or the “average” reinsurance price. Each contract must be
individually priced to meet the particular needs and risk level of the reinsured. This
leads to what might be called the “pricing paradox”:
If you can precisely price a given contract, the ceding company will not want to
buy it.
That is to say, if the historical experience is stable enough to provide data to make a
precise expected loss estimate, then the reinsured would be willing to retain that risk.
As such, the “basic” pricing tools are usually only a starting point in determining an
adequate premium. The actuary proves his or her worth by knowing when the
assumptions in these tools are not met and how to supplement the results with
additional adjustments and judgment.
For the different types of reinsurance outlined in this study note, the basic pricing tools
will be introduced in Section A, and criticisms and advanced topics will be introduced in
Section B. Section A will include the methods generally accepted and standard
throughout the industry. Section B will include areas which require the actuary’s
expertise but have not been solved to universal agreement.
This study note will focus on domestic treaty covers. Pricing for facultative covers or
international (non-U.S.) treaties will not be addressed explicitly, but may be viewed as
variations on the same themes. Differences exist in accounting, loss sensitive features
and the amount of judgment needed, but the underlying theory does not change.
Finally, this study note will give numerical examples where needed. The numbers used
are meant to illustrate the pricing techniques with realistic amounts, but in no way should
be taken as recommendations for actual factors.
Page 2 of 52
1. Proportional Treaties
Section 1A. Basic Tools
A proportional treaty is an agreement between a reinsurer and a ceding company (the
reinsured) in which the reinsurer assumes a given percent of losses and premium. The
simplest example of a proportional treaty is called “Quota Share”. In a quota share
treaty, the reinsurer receives a flat percent, say 50%, of the premium for the book of
business reinsured. In exchange, the reinsurer pays 50% of losses, including allocated
loss adjustment expenses, on the book. The reinsurer also pays the ceding company a
ceding commission which is designed to reflect the differences in underwriting expenses
incurred.
Another, somewhat more complicated, proportional treaty is known as “Surplus Share”;
these are common on property business. A surplus share treaty allows the reinsured to
limit its exposure on any one risk to a given amount (the “retained line”). The reinsurer
assumes a part of the risk in proportion to the amount that the insured value exceeds the
retained line, up to a given limit (expressed as a multiple of the retained line, or
“number” of lines). An example should make this clear:
Retained Line:
1st Surplus:
Risk
Insured Value
1
2
3
4
5
6
50,000
100,000
250,000
500,000
1,000,000
10,000,000
$100,000
4 lines ($400,000)
1st Surplus
Retained
Reinsured 1st Surplus
Portion
Portion
Percent
50,000
100,000
100,000
100,000
100,000
100,000
0
0
150,000
400,000
400,000
400,000
0%
0%
60%
80%
40%
4%
It is important to remember that this is not excess insurance. The retained line is only
being used to establish the percent of the risk reinsured. Once the ceded percent is
calculated, the reinsurer is responsible for that percent of any loss on the risk.
Other types of proportional treaties include fixed and variable quota share arrangements
on excess business (e.g., commercial umbrella policies). For these contracts, the
underlying business is excess of loss, but the reinsurer takes a proportional share of the
ceding company’s book. Umbrella treaties will be addressed in the section on casualty
excess contracts.
Page 3 of 52
The present section will focus primarily on a proportional property treaty. Most of the
techniques described follow standard ratemaking procedures.
The following steps should be included in the pricing analysis for proportional treaties:
Step 1: Compile the historical experience on the treaty.
Assemble the historical premium and incurred losses on the treaty for five or more
years. If this is not available, the gross experience (i.e., prior to the reinsurance
treaty) should be adjusted “as if” the surplus share terms had been in place, to
produce the hypothetical treaty experience. Because a surplus share treaty
focuses on large risks, its experience may be different than the gross experience.
The treaty may be on a “losses occurring” basis for which earned premium and
accident year losses should be used. Alternatively, the treaty may be on a “risks
attaching” basis, which covers losses on policies written during the treaty period.
For risks attaching treaties, written premium and the losses covered by those
policies are used.
Step 2: Exclude catastrophe and shock losses.
Catastrophe losses are due to a single event, such as a hurricane or earthquake,
which may affect a large number of risks. Shock losses are any other losses,
usually affecting a single policy, which may distort the overall results. For
property contracts, catastrophes are generally defined on a per-occurrence
(multiple risk) basis, whereas shock losses are large losses due to a single risk.
For casualty contracts, catastrophes may include certain types of claims
impacting many insureds (e.g., environmental liability), whereas shock losses
would represent a large settlement on a single policy.
Step 3: Adjust experience to ultimate level and project to future period.
The historical losses need to be developed to an ultimate basis. If the treaty
experience is insufficient to estimate loss development factors, data from other
sources may need to be used. Depending on the source of these factors,
adjustments for the reporting lag to the reinsurer or the accident year / policy year
differences may need to be made.
The next step is to adjust historical premiums to the future level. The starting
point is historical changes in rates and average pricing factors (e.g., changes in
schedule rating credits). Rate level adjustment factors can be calculated using
the parallelogram method for “losses occurring” treaties. The impact of rate
Page 4 of 52
changes anticipated during the treaty period must also be included. This is an
area requiring some judgment, as these percents may not actually have been
filed or approved at the time the treaty is being evaluated.
If the premium base is insured value (for property), or some other inflation
sensitive base, then an exposure inflation factor should also be included in the
adjustment of historical premium.
Finally, the losses need to be trended to the future period. Various sources are
available for this adjustment, including the amounts used in the ceding company’s
own rate filings.
Step 4: Select the expected non-catastrophe loss ratio for the treaty.
If the data used in Step 3 is reliable, the expected loss ratio is simply equal to the
average of the historical loss ratios adjusted to the future level. It is worthwhile
comparing this amount to the ceding company’s gross calendar year experience,
available in its Annual Statement, and to industry averages.
Step 5: Load the expected non-catastrophe loss ratio for catastrophes.
Typically, there will be insufficient credibility in the historical loss experience to
price a loading for catastrophe potential. However, this amount is critical to the
evaluation of property treaties.
In the past, reinsurers had priced catastrophe loads based on “spreading” large
losses over expected payback periods. A 1-in-20-year event would be included
as a loading of 5% of the loss amount. The payback approach may still be used
for casualty events but is only referenced as a reasonability check for property.
The most common procedure is now for a company to select a property
catastrophe load based on an engineering-based model that incorporates the risk
profile of the ceding company. These models will be discussed in Section 5A
below.
Step 6: Estimate the combined ratio given ceding commission and other expenses.
After the total expected loss ratio is estimated, the other features of the treaty
must be evaluated. These include:
1. Ceding Commission – often on a “sliding scale” basis (see Section 1B)
2. Reinsurer’s general expenses and overhead
3. Brokerage fees (where applicable)
Page 5 of 52
If the reinsurer’s business is produced through a broker, there is typically a fee
paid by the reinsurer as a percent of treaty premium. If the reinsurer markets the
business directly to the ceding company, there is no brokerage fee, but the
general expense loading may be higher.
Finally, the reinsurer must evaluate whether or not the projected combined ratio
on the treaty is acceptable. The evaluation of treaty terms should take into
account potential investment income and the risk level of the exposures to
determine if they meet the target return of the reinsurer.
The remainder of this section will be devoted to an example of the pricing for a
proportional treaty.
The ceding company has requested a property quota share treaty effective 1/1/97, to be
written on a “losses occurring” basis. The submission includes six years of historical
experience, rate changes, and a loss development triangle.
The first step involves compiling the historical experience, which in this case is six years
with a partial period for 1996. The incurred losses shown are on an accident year basis
and include case reserves and allocated loss adjustment expenses but do not include
IBNR.
Accident Year Experience evaluated 9/30/96:
Accident
Year
Earned
Premium
Incurred
Losses
Loss Ratio
to date
1991
1992
1993
1994
1995
1996
1,640,767
1,709,371
1,854,529
1,998,751
2,015,522
1,550,393
925,021
2,597,041 *
1,141,468
1,028,236
999,208
625,830
56.4%
151.9%
61.6%
51.4%
49.6%
40.4%
Total
10,769,333
7,316,804
67.9%
*Includes 1,582,758 due to Hurricane Andrew
The catastrophe loss for Hurricane Andrew is identified in the 1992 period.
Page 6 of 52
The losses, excluding the Andrew loss, are trended at 4% a year and developed to an
ultimate basis. The development factor on the 1996 year is selected so as to project
losses for the full year.
Accident
Year
Incurred
Losses
(excl. cats)
1991
1992
1993
1994
1995
1996
925,021
1,014,283
1,141,468
1,028,236
999,208
625,830
Total
5,734,046
LDF
Trend
Factor
at 4%
Trended
Ultimate
Incurred
Losses
1.000
1.000
1.000
1.000
1.075
1.600
1.265
1.217
1.170
1.125
1.082
1.040
1,170,152
1,234,382
1,335,518
1,156,766
1,162,229
1,041,381
7,100,428
In addition, the rate change information shown below is provided. It should be noted
that the +10% rate increase to be effective 4/1/97 is an estimate based on the rate filing
that the ceding company expects to make in the coming year. The rate level adjustment
assumes that this amount will be approved.
Effective
Date
1/1/1991
1/1/1993
7/1/1994
4/1/1997
Average
Rate Change
2.00%
10.00%
-4.00%
10.00% (pending)
The earned premium amounts above are then adjusted to the average 1997 rate level
using factors based on a standard parallelogram method. The other adjustments are
that the 1996 premium has been adjusted from a 9 month basis to a full year basis, and
all premiums are trended based on average property value inflation of 3%.
Page 7 of 52
Accident
Year
Unadjusted
Earned
Premium
On Level
Factor
Trend
Factor
at 3%
Earned
Premium
at 1997
Level
1991
1992
1993
1994
1995
1996
1,640,767
1,709,371
1,854,529
1,998,751
2,015,522
2,067,191
1.096
1.086
1.034
0.992
1.023
1.028
1.194
1.159
1.126
1.093
1.061
1.030
2,147,147
2,151,541
2,159,198
2,167,158
2,187,654
2,188,825
Total
11,286,131
13,001,523
The non-catastrophe loss ratio is estimated to be 54.6% based on the projections of loss
and premium to the 1997 level.
Accident
Year
Earned
Premium
at 1997
Level
Trended
Ultimate
Incurred
Losses
Projected
Loss Ratio
1991
1992
1993
1994
1995
1996
2,147,147
2,151,541
2,159,198
2,167,158
2,187,654
2,188,825
1,170,152
1,234,382
1,335,518
1,156,766
1,162,229
1,041,381
54.5%
57.4%
61.9%
53.4%
53.1%
47.6%
Total
13,001,523
7,100,428
54.6%
The loading for catastrophe losses now needs to be made. For the historical period, the
catastrophe loss associated with Hurricane Andrew would have added about 15% to the
loss ratio if it had not been excluded. A loading from a catastrophe model might add in a
smaller amount. For our example, we will assume that we have selected a 10% loading
for catastrophe losses, making our final expected loss ratio approximately 65%.
The final step in the evaluation is the determination of the reinsurer’s combined ratio. A
ceding commission of 30% has been suggested by the reinsured. The other expenses
are listed below:
Page 8 of 52
Expected Loss Ratio
Ceding Commission
Brokerage fees
Administrative expenses
Unallocated expenses
65.0%
30.0%
5.0%
1.0%
1.0%
Indicated Combined Ratio
102.0%
The reinsurance actuary must then evaluate the profitability of these proposed terms. A
102% combined ratio is unlikely to produce an acceptable return for the reinsurer so a
reduction in the ceding commission may be the actuary’s recommendation. Other
provisions, such as a loss occurrence limit or adjustable features (discussed in the next
section) may also be considered.
Section 1B. Special Features of Proportional Treaties
After the expected loss ratio is estimated for a proportional treaty, the actuary’s work is
not yet done. There will often remain disagreement between the ceding company and
reinsurer about the loss ratio and the appropriate ceding commission. In theory, a
reinsurer should “follow the fortunes” of the ceding company, but in practice their results
may be quite different. Reinsuring a profitable insurer is no guarantee of profits for the
reinsurer. In the negotiations to resolve these differences, adjustable features are often
built into the treaty.
a) Sliding Scale Commission
A common adjustable feature is the “sliding scale” commission. A sliding scale
commission is a percent of premium paid by the reinsurer to the ceding company which
“slides” with the actual loss experience, subject to set minimum and maximum amounts.
For example:
Given the following commission terms:
Provisional Commission:
30%
Minimum Commission:
Sliding 1:1 to
Sliding .5:1 to a Maximum
25% at a 65% loss ratio
35% at a 55% loss ratio
45% at a 35% loss ratio
Page 9 of 52
Then the results may follow, for different loss scenarios,
Actual
Loss Ratio
30% or below
35%
40%
45%
50%
55%
60%
65% or above
Adjusted
Commission
45.0%
45.0%
42.5%
40.0%
37.5%
35.0%
30.0%
25.0%
In a “balanced” plan, it is fair to simply calculate the ultimate commission for the
expected loss ratio. However, this may not be appropriate if the expected loss ratio is
towards one end of the slide. For example, if the expected loss ratio is 65%, the
commission from a simple calculation is 25%, producing a 90% technical ratio (i.e., the
sum of the loss and commission ratios). If the actual loss ratio is worse than 65%, the
reinsurer suffers the full amount, but if the actual loss ratio is better than 65%, the
reinsurer must pay additional commission.
It is more correct to view the loss ratio as a random variable and the expected loss ratio
as the probability-weighted average of all possible outcomes. The expected ultimate
commission ratio is then the average of all possible outcomes based on the loss ratio.
The simplest approach is to estimate the expected commission based on the historical
loss ratios, adjusted to future level as above but including the catastrophe and shock
losses. This is a good calculation to make as a reasonability check but may be distorted
by historical catastrophes or years with low premium volume. It also leaves out many
possible outcomes.
A better approach is the use of an aggregate loss distribution model. Several models
are available and these are described in Section 4. The results of any of these models
may be put into the following format:
Page 10 of 52
Range of
Loss Ratios
Average
Loss Ratio
in Range
Probability
of being
in Range
Sliding
Scale
Commission
0% – 35%
35% – 55%
55% – 65%
65% or above
31.5%
46.9%
59.9%
82.2%
0.025
0.311
0.222
0.442
45.0%
39.0%
30.1%
25.0%
0% or above
65.0%
1.000
31.0%
Note that in this example, the expected technical ratio is 96% (=65%+31%) rather than
the 90% (=65%+25%) naively estimated above.
A further complication is the introduction of a carryforward provision in the commission.
A carryforward provision allows that if the past loss ratios have been above the loss ratio
corresponding to the minimum commission, then the excess loss amount can be
included with the current year’s loss in the estimate of the current year’s commission. In
the long run, this should help smooth the results.
Two approaches may be taken to pricing the impact of carryforward provisions. The first
is to include any carryforward from past years and estimate the impact on the current
year only. This amounts to shifting the slide by the amount of the carryforward. For
example, if the carryforward from prior years amounts to a 5% addition to the loss ratio,
the terms above would become:
Minimum Commission:
Sliding 1:1 to
Sliding .5:1 to a Maximum
25% at a 60% current year loss ratio
35% at a 50% current year loss ratio
45% at a 30% current year loss ratio
The analysis above would then be restated as follows:
Range of
Loss Ratios
Average
Loss Ratio
in Range
Probability
of being
in Range
Sliding
Scale
Commission
0% – 30%
30% – 50%
50% – 60%
60% or above
27.4%
43.0%
55.1%
78.3%
0.006
0.221
0.222
0.551
45.0%
38.5%
29.9%
25.0%
0% or above
65.0%
1.000
29.2%
Page 11 of 52
The problem with this approach is that it ignores the potential for carryforward beyond
the current year. For example, in the first year of the program we would calculate the
expected commission for the current year as though the program would be cancelled at
the end of the year. The same price would result with or without the carryforward
provision – which does not seem right because the benefit of the carryforward is ignored.
A second approach is to look at the “long run” of the contract. The sliding scale is
modeled as applying to a longer block of years rather than just the single current year.
The variance of the aggregate distribution would be reduced on the assumption that
individual bad years would be smoothed by good experience on other years. The
variance of the average loss ratio for a block of years should be significantly less than
the variance of the loss ratio for a single year (roughly equal to dividing by the number of
years in the block). As an example:
Range of
Loss Ratios
Average
Loss Ratio
in Range
Probability
of being
in Range
Sliding
Scale
Commission
0% – 35%
35% – 55%
55% – 65%
65% or above
34.1%
51.6%
60.4%
72.3%
0.000
0.118
0.408
0.474
45.0%
36.7%
29.6%
25.0%
0% or above
65.0%
1.000
28.3%
This example reduces the aggregate variance, putting greater probability in the ranges
closer to the expected loss ratio of 65%. The first problem with this approach is that the
method for reducing the variance is not obvious; the example above reduces the
standard deviation of the aggregate distribution by the square root of 5, assuming that
the commission applies to a five-year block. A second problem is that it ignores the fact
that the contract may not renew the following year, potentially leaving the reinsured with
no carryforward benefit.
This issue is further complicated when a commission deficit can be carried forward but
not a credit. There is no standard method for handling these questions so far as this
author is aware.
b) Profit Commission
A profit commission subtracts the actual loss ratio, ceding commission and a “margin”
for expenses from the treaty premium and returns a percent of this as additional
commission. For example:
Page 12 of 52
Actual Loss Ratio
Ceding Commission
Margin
Reinsurer’s Profit
55%
25%
10%
10% (100%-55%-25%-10%)
Percent Returned
Profit Commission
50% (as a percent of Reinsurer’s Profit)
5% (10% profit times 50%)
Like the sliding scale commission, this should be evaluated using an aggregate
distribution on the loss ratio. Also like the sliding scale commission, there is some
ambiguity concerning the handling of carryforward provisions.
c) Loss Corridors
A loss corridor provides that the ceding company will reassume a portion of the
reinsurer’s liability if the loss ratio exceeds a certain amount. For example, the corridor
may be 75% of the layer from an 80% to a 90% loss ratio. If the reinsurer’s loss ratio is
100% before the application of the loss corridor, then it will have a net ratio of 92.5%
after its application, calculated as:
Before
Corridor
After
Corridor
Below corridor
Within corridor
Above corridor
80.0%
10.0%
10.0%
80.0%
2.5%
10.0%
Total Loss Ratio
100.0%
92.5%
100% capped at 80%
10% minus 75% of 90%-80%
100% minus 90%
As above, the proper estimate of the impact of the loss corridor should be made using
an aggregate distribution. The probability and expected values for the ranges below,
within and above the corridor can be evaluated.
Range of
Loss Ratios
Average
Loss Ratio
in Range
Probability
of being
in Range
Loss Ratio
Net of Loss
Corridor
0% – 80%
80% – 90%
90% or above
64.1%
84.7%
103.9%
0.650
0.156
0.194
64.1%
81.2%
96.4%
0% or above
75.0%
1.000
73.0%
Page 13 of 52
For this example, the expected loss ratio is 75.0% before the application of the loss
corridor. Even though this is less than the 80% attachment point for the corridor, the
corridor still has the effect of lowering the reinsurer’s expected loss ratio.
Many variations on these features can be used with a proportional treaty. Bear and
Nemlick [1] provide further background on handling loss sensitive features. This should
serve to illustrate that the actuary’s job is not finished after the expected loss ratio is
calculated.
2. Property Per Risk Excess Treaties
Section 2A. Experience and Exposure Rating Models
Property per risk excess treaties provide a limit of coverage in excess of the ceding
company’s retention. The layer applies on a “per risk” basis, which typically refers to a
single property location. This is narrower than a “per occurrence” property excess treaty
which applies to multiple risks to provide catastrophe protection.
The treaty premium is set as a percent of a subject premium base. The subject
premium goes by the oxymoronic title “gross net earned premium income” (GNEPI) for
losses occurring policies or “gross net written premium income” (GNWPI) for risks
attaching policies. This premium is net of any other reinsurance inuring to the benefit of
the per risk treaty, such as a surplus share treaty, but gross of the per risk treaty being
priced.
The main tools available for pricing per risk treaties are experience and exposure rating.
a) Experience Rating
Experience rating is sometimes referred to as a “burn cost” model though that phrase
more commonly denotes just the unadjusted experience and not the projected cost. The
basic idea of experience rating is that the historical experience, adjusted properly, is the
best predictor of future expectations. The analysis proceeds as follows:
Step 1:
Gather the subject premium and historical losses for as many recent years as
possible. Ten years should be sufficient, though the number of years relied upon
in the final analysis should be a balance between credibility and responsiveness.
Page 14 of 52
The historical losses should include all losses that would pierce the layer being
priced after the application of trend factors.
Step 2:
Adjust the subject premium to the future level using rate, price and exposure
inflation factors as outlined in the section on proportional treaties.
Step 3:
Apply loss inflation factors to the historical large losses and determine the amount
included in the layer being analyzed. Sum up the amounts which fall in the layer
for each historical period. If allocated expense (ALAE) applies pro-rata with
losses, it should be added in individually for each loss.
Step 4:
Apply excess development factors to the summed losses for each period. As in
any experience rating model, the loss development factors should be derived
from the same ceding company data if possible. Along with the LDF, frequency
trend, if determined to be needed, should be applied at this step.
Step 5:
Dividing the trended and developed layer losses by the adjusted subject premium
produces loss costs by year. These may be averaged to project the expected
loss cost.
The projected loss costs from this analysis should be randomly distributed about the
average. If the loss costs are increasing or decreasing from the earliest to latest years
in the experience period, then the assumptions of the model may need to be
reexamined. The trend or development factors may be too high or low. Alternatively,
there may have been shifts in the types of business or sizes of risks written by the
ceding company.
As an example of experience rating for a property excess of loss treaty, assume the
following terms are requested:
Effective Date:
Treaty Limit:
Attachment Point:
1/1/97
$400,000
$100,000
Page 15 of 52
The losses shown below have been recorded for the treaty. For each loss, a 4% annual
trend rate is applied to project the loss from its accident date to the average date in the
prospective period. For each trended loss, we then calculate the portion that penetrates
into the treaty layer being priced.
Accident
Date
Untrended
Total Loss
Trend
Factor
at 4%
Trended
Total Loss
Loss in
Treaty
Layer
9/20/1988
10/11/1988
3/15/1989
6/21/1990
10/24/1990
1/10/1991
2/23/1992
4/30/1992
9/22/1992
1/1/1993
5/18/1993
8/1/1993
8/15/1994
7/12/1995
240,946
821,499
158,129
114,051
78,043
162,533
324,298
100,549
75,476
171,885
94,218
170,297
87,133
771,249
1.411
1.408
1.385
1.317
1.300
1.289
1.234
1.225
1.206
1.193
1.175
1.166
1.119
1.080
339,975
1,156,671
219,009
150,205
101,456
209,505
400,184
123,173
91,024
205,059
110,706
198,566
97,502
832,949
239,975
400,000
119,009
50,205
1,456
109,505
300,184
23,173
0
105,059
10,706
98,566
0
400,000
The losses that trend into the proposed layer are then summed for each historical
accident year. The subject premium for each year is listed after adjustment for rate level
changes and inflation trend of the insured values. The application of the loss
development factor projects the ultimate trended loss cost for the treaty.
Page 16 of 52
Accident
Year
On Level
Subject
Premium
Trended
Losses
in Layer
1988
1989
1990
1991
1992
1993
1994
1995
1,422,554
1,823,103
2,054,034
2,147,147
2,151,541
2,159,198
2,167,158
2,187,654
639,975
119,009
51,661
109,505
323,357
214,331
0
400,000
Total
16,112,389
1,857,838
LDF
Trended
Ultimate
in Layer
Loss
Cost
1.000
1.000
1.000
1.000
1.010
1.050
1.150
1.300
639,975
119,009
51,661
109,505
326,591
225,048
0
520,000
45.0%
6.5%
2.5%
5.1%
15.2%
10.4%
0.0%
23.8%
1,991,789
12.4%
b) Exposure Rating
The second pricing tool for property per risk treaties is exposure rating. The advantage
of this approach over experience rating is that the current risk profile is modeled, not
what was written years earlier. The exposure rating model is fairly simple, but may at
first appear strange since nothing similar is found on the primary insurance side.
The approach was first developed by Ruth Salzmann in 1963 for Homeowners business
and eventually adapted for commercial property as well. The method centers on an
exposure curve (P). This represents the amount of loss capped at a given percent (p) of
the insured value (IV) relative to the total value of the loss. This may be represented
mathematically as:
·
·
·
·
·
·
1
·
where f(x) = distribution of individual loss dollar amount
For a property of a given insured value, we calculate the retention and limit as percents
of that insured value. The portion of the expected loss on the risk which falls in the
treaty layer is then given by:
P((Retention+Limit)/Insured Value) – P(Retention/Insured Value)
Page 17 of 52
As an example, suppose the proposed treaty is intended to cover a per-risk layer of
$400,000 excess of $100,000. For a single risk with an insured value of $500,000, we
would calculate the difference between the exposure factors for 20% (from $100,000 /
$500,000) and 100% (from $400,000+$100,000 / $500,000). From the table below, this
results in an exposure factor of 44% (= 93%-49%).
Percent
of I.V.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
110%
120%
Exposure
Factor
0%
37%
49%
57%
64%
70%
76%
81%
85%
89%
93%
97%
100%
The exposure curve provided above is for illustration purposes only. The curve does
allow for exposure above the insured value; this is due to the fact that often the limits
profile provided does not include business interruption coverage for commercial policies
or living expenses for homeowners policies.
For a portfolio of risks, this same calculation is performed on a distribution of premium
by different ranges of insured values, known as the “limits profile”. The limits profile
must also be questioned to verify that the size of risk ranges are on a per location basis.
If it is assembled using total values for policies covering multiple locations, distortions
will result.
For the example below, it is assumed that all locations within the range are exactly equal
to the midpoint of the range.
Treaty Limit:
Treaty Retention:
$400,000
$100,000
Page 18 of 52
Range of Insured
Values ($000s)
20 – 100
100 – 250
250 – 1,000
1,000 – 2,000
Midpoint
Retention as
% of I.V.
Ret+Limit
% of I.V.
Exposure
Factor
60
175
625
1,500
167%
57%
16%
7%
833%
286%
80%
33%
0%
26%
41%
33%
Range of Insured
Values ($000s)
Subject
Premium
Expected
Loss Ratio
Expected
Losses
Reinsurer’s
Losses
20 – 100
100 – 250
250 – 1,000
1,000 – 2,000
682,000
161,000
285,000
1,156,000
65%
65%
65%
65%
443,300
104,650
185,250
751,400
0
27,209
75,953
247,962
Grand Total
2,284,000
65%
1,484,600
351,124
The reinsurer’s loss cost is 15.37% (Reinsurer’s Losses 351,124 over Subject Premium
2,284,000). This loss cost is then loaded for expenses and profit.
The expected loss ratio is of critical importance as the final rate will move proportionally
with this amount. A rigorous projection of the expected loss ratio, following the
procedures for proportional treaties, should be made.
An implicit assumption in the exposure rating approach outlined above is that the same
exposure curve applies regardless of the size of the insured value. For example, the
likelihood of a $10,000 loss on a $100,000 risk is equal to the likelihood of a $100,000
loss on a $1,000,000 risk. This assumption of scale independence may be appropriate
for homeowners business, for which this technique was first developed, but may be a
serious problem when applied to large commercial risks. The Lloyds scales, previously
an industry standard, did not recognize this shortcoming.
Ludwig [4] gives an excellent, more detailed description of this topic.
Section 2B. Other Issues on Property Per Risk Treaties
After loss costs are estimated using the experience and exposure rating models, the
actuary’s task is to reconcile the results and select a final expected loss cost.
Page 19 of 52
a) Free Cover
One difficulty in this reconciliation is the issue of “free cover”. This refers to an
experience rating in which no losses trend into the highest portion of the layer being
priced. For example, if you are comparing prices for a layer $750,000 excess of
$250,000 with a layer $250,000 excess of $250,000, and your largest trended loss is
$500,000 from ground up, then you will produce the same loss cost for either option.
The top $500,000 excess of $500,000 layer would be implicitly a “free cover”. One
approach to this problem is to use the experience rating as a basis for the lowest portion
of the layer and then use the relativities in the exposure rating to project the higher layer.
The table below gives an example of this approach:
Experience
Rating
Loss Cost
Exposure
Rating
Loss Cost
$250k xs $250k
$500k xs $500k
16%
0%
20%
10%
$750k xs $250k
16%
30%
24%
* 8% = 16% ͯ (10%/20%)
Layer to
be Priced
Selected
Loss Cost
16%
8% *
b) Credibility
A first measure of credibility is the number of claims expected during the historical
period. Note that this is not the same as the actual number observed during the period.
If credibility is set based solely on the historical number, then more credibility will be
assigned to experience rating projections that are fortuitously worse than average.
Because the expected number of claims may not be easily calculable, the dollars of
expected loss, based on the exposure rating, may be used. For example, if the
exposure rating indicates that $2,000,000 in losses was expected during the historical
period, but only $1,000,000 was actually observed, then the credibility given to the
experience rating should still be based on the $2,000,000 expected.
As a second measure of credibility, it is appropriate to look at the year-to-year variation
in the projected loss cost from each of the historical periods. Stability in this rate should
add credibility even if the number of claims is relatively small.
Assigning credibility is, in part, a subjective exercise. Often significant credibility is given
to experience rating simply because there are too many limitations to the exposure
Page 20 of 52
rating alternative. Discussions on reconciling the experience and exposure rating results
are given in Mashitz and Patrik [5] and Clark [9].
c) Inuring Reinsurance
An additional problem which may be encountered in both methods is that the excess
treaty may apply to the ceding company’s retention after a surplus share treaty is
applied. The $750k xs $250k layer may apply to a $1,000,000 loss which is actually a
10% share of a $10,000,000 loss. For experience rating, the only accurate way to
reflect this underlying reinsurance is to restate the historical loss experience on a basis
net of the inuring reinsurance.
The exposure rating can be applied directly to a risk profile adjusted to reflect the terms
of the inuring surplus share treaty. However, if the actuary has exposure curves varying
by size of insured value, the curve should be selected based on the insured value before
the surplus share is applied, but the exposure factor should apply to the subject
premium after the surplus share is applied.
For example, suppose the ceding company from Section 2A decides to purchase a
surplus share treaty in which it retains a maximum of $200,000 on any one risk. On its
net retention, it then wishes to purchase a per-risk excess cover of $100,000 excess of
$100,000. Its risk profile and the single exposure rating curve are the same as used in
the earlier example.
Range of Insured
Values ($000s)
Midpoint
Ins. Value
after S/S
Gross
Premium
GNEPI
20 – 100
100 – 250
250 – 1,000
1,000 – 2,000
60
175
625
1,500
60
175
200
200
682,000
161,000
285,000
1,156,000
682,000
161,000
91,200
154,133
2,284,000
1,088,333
Grand Total
Range of Insured
Values ($000s)
Net
Ins. Value
Retention
% of I.V.
Ret+Limit
% of I.V.
Exposure
Factor
20 – 100
100 – 250
250 – 1,000
1,000 – 2,000
60
175
200
200
167%
57%
50%
50%
333%
114%
100%
100%
0%
24%
23%
23%
Page 21 of 52
Range of Insured
Values ($000s)
Subject
Premium
Expected
Loss Ratio
Expected
Losses
Reinsurer’s
Losses
20 – 100
100 – 250
250 – 1,000
1,000 – 2,000
682,000
161,000
91,200
154,133
65%
65%
65%
65%
443,300
104,650
59,280
100,186
0
25,116
13,634
23,043
Grand Total
1,088,333
65%
707,416
61,793
The loss cost for the $100,000 excess of $100,000 layer is 5.68% (Reinsurer’s Losses
61,793 over Subject Premium 1,088,333) for the per-risk excess treaty net of the surplus
share. The exposure factors for the two highest ranges are the same because a single
exposure curve is used.
3. Casualty Per Occurrence Excess Treaties
Section 3A. Experience and Exposure Rating Models
Like property excess, casualty lines use experience and exposure rating models. This
discussion of casualty will refer to general liability (including products), auto liability and
workers compensation. The same techniques described can be adapted for other
casualty lines, such as professional liability, with some modifications.
Casualty per occurrence excess treaties are often separated into three categories:
Working Layer:
Low layer attachment which is expected to be penetrated, often multiple
times in each annual period.
Exposed Excess:
Excess layer which attaches below some of the policy limits on the
underlying business – that is, there are policies for which a full limit loss
would cause a loss to the treaty. Typically, these losses will be less
frequent and there will be some years in which the treaty layer is not
penetrated.
Clash Covers:
High layer attachment excess – typically a loss on a single policy will not
penetrate the treaty layer. A clash cover will be penetrated due to multiple
policies involved in a single occurrence, or when extra-contractual
obligations (ECO) or rulings awarding damages in excess of policy limits
Page 22 of 52
(XPL) are determined in a settlement. The method for including allocated
loss adjustment expenses in the treaty may also expose the clash layer.
The distinctions between these categories are generally soft in the pricing process. A
perfect working layer would produce stable enough results to be retained by the ceding
company. Experience rating techniques are still used even when the experience
approaches the “exposed excess” category. On the other hand, for large ceding
carriers, “clash” losses may be common enough that the experience rating procedure
provides guidance for the price.
a) Experience Rating
The steps in the experience rating procedure follow those of property experience rating,
but some additional complications arise.
Step 1:
Gather the subject premium and historical losses for as many years as possible. Along
with the historical losses, it is very important that allocated loss adjustment expenses
(ALAE) be captured separately from losses. For general liability and auto liability losses,
the underlying policy limit should also be listed. For auto losses on a split limits rather
than a combined single limit (CSL) basis, other modifications may be needed in order to
separately cap losses for bodily injury and property damage.
Workers compensation (WC) losses will not have an explicit limit associated with them.
However, because large workers compensation losses are often shown on a discounted
case reserve basis, a request should be made for these losses on a full undiscounted
basis. Further discussion of handling WC losses will be given in the next section.
Step 2:
Adjust the subject premium to the future level using rate, price and exposure inflation
factors. These adjustment factors will vary for each line of business included.
Step 3:
Apply loss inflation factors to the individual historical losses. Inflation factors should also
vary by line of business.
The selection for a source of loss inflation is difficult. The Insurance Services Office
(ISO) estimates basic and total limits trend factors for general and auto liability for use in
Page 23 of 52
ratemaking. Theoretically, what should be used is an unlimited trend factor derived from
large losses only. Using losses capped at the underlying policy limit as a source may
understate the final results. There is also an implicit assumption that the same trend
factor applies to all losses regardless of amount. In the final analysis, the actuary must
make a selection of loss inflation rates by year.
The trended losses must then be capped at applicable policy limits. This represents
another problem for which there is no generally accepted solution. Theoretically, we
want to cap losses at the limit applicable if the same policy were written in the future
treaty period. One possible approach is to apply the historical policy limit to each
trended loss; this leaves out the fact that the insured will generally increase its policy
limits over time. A second approach is to apply the trend factor to the historical loss
without applying a policy limit cap; this assumes that policy limits “drift” upwards to
precisely match inflation. If this second approach is used, then the subject premium
must also be adjusted to the level that would have been charged had the higher limits
been in effect; otherwise an overstatement of the expected loss cost will result.
The discussion by Mata and Verheyen [10] gives some more advanced concepts on
making use of exposure rating techniques to adjust for changes in the policy limit profile.
After the loss and ALAE amounts are trended, the portion of each in the treaty layer is
calculated. Allocated expenses are usually included in one of two ways:
Pro-rata with loss:
ALAE in the layer allocated in proportion to losses.
ALAE as Part-of-Loss (aka “on top” or “add-on”):
ALAE added to loss and the treaty limit applies to the sum.
Example 1:
Trended Loss:
Trended ALAE:
Treaty Attachment:
Treaty Limit:
$640,000
$320,000
$400,000
$600,000
Page 24 of 52
Pro-Rata Treatment of ALAE
Loss
ALAE
Loss+ALAE
ALAE as
Part-of-Loss
Loss+ALAE
Retained
In Treaty
Above Treaty
400,000
240,000
0
200,000
120,000
0
600,000
360,000
0
400,000
560,000
0
Total
640,000
320,000
960,000
960,000
Pro-Rata Treatment of ALAE
Loss
ALAE
Loss+ALAE
ALAE as
Part-of-Loss
Loss+ALAE
Example 2:
Trended Loss:
Trended ALAE:
Treaty Attachment:
Treaty Limit:
$920,000
$460,000
$400,000
$600,000
Retained
In Treaty
Above Treaty
400,000
520,000
0
200,000
260,000
0
600,000
780,000
0
400,000
600,000
380,000
Total
920,000
460,000
1,380,000
1,380,000
These two examples should serve to illustrate the two methods of including ALAE in a
treaty. It should also be noted that the amount in the treaty layer is not necessarily
higher or lower for either method, but depends on the actual experience.
Step 4:
Apply excess development factors to the summed losses for each period. For casualty
lines, this step is critical due to the very large factors needed to reflect future
development. If possible, historical patterns should be derived for the excess layer
using ceding company data. Where this is not available, other benchmarks are needed.
The Reinsurance Association of America (RAA) publishes a loss development study on
a biennial basis, which is considered an industry benchmark. The historical data in that
study includes more than thirty years of development, broken out by line of business. Its
statistics show a significant lag between reported losses for a primary company and a
Page 25 of 52
reinsurer. The graphs included in the 2012 edition of the RAA Study, attached as a
supplement to this study note, illustrate this lag.
The use of compiled industry data gives a level of stability to the estimate of excess
development patterns that is often superior to that for individual ceding companies.
While the RAA statistics may be considered a benchmark, the user should remember
that the data is simply what is reported by its members. Some cautions:
1. The reporting lag from the occurrence of an event to the establishment of a
reinsurer’s case reserve may vary by company. Included in the data is
retrocessional business which may include several levels of reporting lag.
2. The mix of attachment points and limits is not cleanly broken out. In recent
studies, the RAA has begun publishing statistics by attachment point ranges, but
this data is considerably less stable than the total triangle. Loss development
varies significantly for different attachment points so every effort should be made
to adjust the selected factors to the layer of the treaty being priced.
3. The RAA requests data exclusive of Asbestos and Environmental claims which
could distort the patterns. It cannot be known if all member companies have
done this consistently. Other long term exposure claims, such as medical
products, mold, or tobacco, are not excluded.
4. For workers compensation, the members may not handle the tabular discount
on large claims in a consistent manner. If a ceding company reports a loss on a
discounted basis, and the reinsurer establishes a case reserve as the amount of
the discounted value that falls into the reinsured layer, a very high development
factor may result due to the unwinding of the discount.
As a practical matter, having a very slow development pattern will often produce results
showing either zero or very high projected ultimate layer losses by year. The actuary
will often need to use smoothing techniques, such as a Bornhuetter-Ferguson approach
or Cape Cod (aka Stanard-Bühlmann), to produce a final experience rate.
Step 5:
Dividing the trended and developed layer losses by the adjusted subject premium
produces loss costs by year. These amounts are averaged and a final expected loss
cost selected. The loss cost may be adjusted for the time value of money, expenses
and risk load; these adjustments are dealt with in the last section of this study note.
Page 26 of 52
b) Exposure Rating
The second pricing method is exposure rating. As was the case for property, this
method estimates a loss cost based on the premium and limits expected to be exposed
during the treaty period. The exposure rating approach uses a severity distribution,
based on industry statistics, to estimate layer losses. The severity distribution is used to
calculate increased limits factors (ILF) for general liability and auto liability, and excess
loss factors (ELF) for workers compensation. The theory is the same for these different
lines, but the practical calculation is different.
For all of these approaches, we begin with a Cumulative Distribution Function (CDF)
representing the probability that a loss is a given size or smaller.
x=
F(x) =
f(x) =
E[x] =
E[x;L] =
random variable for size of loss
probability a loss is x or smaller, the CDF
density function, first derivative of F(x)
expected value or average unlimited loss
expected value of losses capped at L
The severity distribution is used to calculate expected losses in any given layer.
We define:
;
,
;
;
,
;
For general liability and auto liability, one option is to use the truncated Pareto
distribution for loss severity. The form of E[x;L] is given by
;
1
·
1
for
·
Q1, L>T.
Page 27 of 52
·
·
The five parameters for this distribution follow some intuitive meanings:
T=
Truncation point, “small” losses are below this point,
“large” losses follow a Pareto distribution
probability of a “small” loss
average small loss severity
scale parameter for Pareto distribution
shape parameter for Pareto distribution
P=
S=
B=
Q=
The scale of the distribution is easily adjusted for inflation by multiplying the parameters
T, S and B by the same amount. Two limitations of this formula should be noted:
1. The formula shown above only applies for losses above the truncation point T.
As a practical matter, this is not a problem as that parameter is set at an amount
well below any treaty attachment point.
2. The excess factors for higher layers become very dependent on the Q parameter.
This parameter must be watched very carefully when the curves are updated.
A curious note on the truncated Pareto distribution is that when B=0 and Q=1, the
distribution becomes a log-logistic distribution of the form below.
;
·
1
·
· 1
This has the property that expected losses in layers are equal if the limit and attachment
point are in the same ratio.
;
;
;
;
for any constant k
This property may be approximated when the B parameter is small and the Q parameter
is close to 1. It should be remembered, however, that this relationship holds for
severities for individual claims, but not necessarily for treaty loss costs, which will
decrease for higher layers due to fewer policies being exposed.
The “BQPST” form of the Pareto is not the only choice available. There is great
flexibility possible with discrete mixture models. A discrete mixture is a weighted
average of relatively simple curve forms that approximates a more complex but realistic
shape.
A popular example of a mixture model is the Mixed Exponential, which is a weighted
average of several exponential distributions.
Page 28 of 52
;
·
· 1
where
1
Once a severity distribution is selected, an exposure factor can be calculated. This
factor is analogous to the factor used for excess property and should likewise be applied
to ground-up expected losses to estimate the loss cost to the treaty layer.
;
Exposure Factor
Where
,
;
,
;
PL = Ceding Company Policy Limit
AP = Treaty Attachment Point
Lim = Treaty Limit
If the treaty includes ALAE in proportion to losses, this exposure factor can be applied to
subject premium times an expected loss and ALAE ratio. If the ALAE is included with
losses, the following exposure factor formula can be used:
;
Exposure Factor
,
;
1
,
1
;
Where:
PL = underlying Policy Limit applying to loss only
AP = Treaty Attachment Point applying to ALAE plus loss capped at PL
Lim = Treaty Limit applying to ALAE plus loss capped at PL
e = ALAE as a percent of loss capped at PL
The key assumption in both cases is that ALAE varies directly with capped indemnity
loss. This is not an accurate model in that ALAE is not a constant percent of any given
loss. For example, losses which close without an indemnity payment may still incur a
large expense. In general, as the size of a loss increases, the ALAE as a percent of the
loss will tend to decrease. The assumption that loss and ALAE are perfectly correlated
will tend to result in an overstatement of expected amounts in the higher layers.
Page 29 of 52
Another limitation of the formula for the latter case is that an exposure factor of zero will
be applied to high layers which are indeed exposed. For example, if the underlying
policy limit is $1,000,000 and the ALAE loading is 1.500, then a treaty attaching at
$1,500,000 will not be considered exposed by this formula.
A more refined analysis of the effect of ALAE would require modeling of how ALAE
varies with loss size.
Another use for the severity curves is for proportional treaties on excess business.
These proportional treaties may be on a quota share basis, where the reinsurer takes a
set percent of each contract the ceding company writes, or on a “cessions” basis for
which the percent depends on the attachment point and limit written on each policy. A
cessions basis treaty will typically require the ceding company to use increased limits
factors to price the portion of its policies exposing the treaty. The exposure factors
calculated above can be compared with the factors used by the ceding company in
pricing its business.
For workers compensation, the severity distributions used most commonly come from
the National Council on Compensation Insurance (NCCI), which publishes excess
factors for retrospective rating plans in many states. Its curves vary by state and hazard
group. The underlying data incorporates different injury types as well. It is not always
possible to calculate the underlying severity distribution directly.
The NCCI curves, or other excess factors, can easily be approximated by an inverse
power curve of the form:
;
·
The parameters “a” and “b” are estimable from selected excess factors. The fitted
factors behave in the higher layers much like the Pareto distribution described above.
Workers compensation does not have policy limits corresponding to those on liability
policies. The WC limits refer instead to limitations on annual benefits specific to
individual states. The exposure factor is therefore calculated using only the treaty
attachment point (AP) and limit.
Exposure Factor = ELFAP – ELFAP+Limit
The exposure factor is estimated separately for each state and hazard group for which
the ceding company projects premium for the treaty period. Expected loss ratios are
also needed for each of these divisions.
Page 30 of 52
An example of exposure rating would look as follows:
Treaty Limit:
Treaty Attachment Point:
750,000
250,000
State
H.G.
Standard
Premium
ELR
ELF at
250,000
ELF at
1,000,000
Exposure
Factor
Treaty
Losses
AL
AL
NJ
NJ
B
C
B
D
100,000
100,000
100,000
100,000
70%
70%
85%
85%
0.030
0.040
0.070
0.100
0.006
0.008
0.020
0.035
0.024
0.032
0.050
0.065
1,680
2,240
4,250
5,525
400,000
13,695
The loss cost for the treaty will be 3.42% (Treaty Losses 13,695 over Standard Premium
400,000).
Section 3B. Special Problems on Casualty Excess Treaties
This section will deal with a number of problems which commonly arise with casualty
excess treaties. Issues about credibility or “free cover” have been addressed in the
section on property per risk excess treaties, but should equally be considered for
casualty treaties. The methods described are the author’s suggestions and should not
be viewed as the consensus opinion. However these issues are addressed, they cannot
be ignored in the pricing process.
a) Including Umbrella Policies
The ceding company may include umbrella policies in the business subject to the treaty.
These policies are excess of an underlying retention and “drop down” if an underlying
aggregate is exhausted.
If the umbrella policies are above primary policies written by the ceding company, then it
is best to consider the combination of the primary and excess as a single policy with a
higher limit. For experience rating the primary and excess pieces are simply added
together. When the umbrella policies are above primary policies from other carriers, the
procedures are more difficult.
Page 31 of 52
For experience rating, the main difficulty is in selecting the appropriate trend factor. The
limit on the underlying policy should be added to losses on the umbrella policy before
the application of trend, then subtracted after it:
Trended Loss = (Loss + Underlying Limit)·(Trend Factor) – Underlying Limit
This procedure will still leave out losses from the underlying policy which historically did
not exhaust the underlying limit, but which would have after the application of a trend
factor.
For exposure rating, the exposure factor on an excess policy is calculated as:
Exposure Factor
;
,
;
;
;
,
Where:
UL = Limit of Underlying Policies (attachment point of the umbrella)
PL = Policy Limit on Umbrella
AP = Treaty Attachment Point
Lim = Treaty Limit
For example, if the ceding company sells an umbrella policy for $1,000,000 excess of
$1,000,000 and the treaty covers losses for the layer $500,000 excess of $500,000,
then the exposure factor would be:
Exposure Factor
;2
;2
; 1.5
;1
The graphic below illustrates how this treaty would apply.
Page 32 of 52
This formula leaves out the possibility of the “drop down” feature of the umbrella policy.
An approximation to include this additional exposure would be:
Exposure Factor
;2
;2
; 1.5 · 1
;1 · 1
;1
;1
; 0.5 ·
0 ·
The Ï• in the formula represents the aggregate excess factor on the underlying policy.
This is analogous to a Table M charge factor, and will be given a more explicit definition
in the section on Aggregate Distributions.
b) Loss Sensitive Features
For working layer excess, the ceding company is often willing to retain more of the
losses. In these cases, an annual aggregate deductible (AAD) may be used. The AAD
allows the ceding company to retain the first losses in the layer, but maintain protection
in case there are more losses than anticipated. The treaty then becomes an excess of
aggregate cover, where the aggregate losses are per occurrence excess losses in the
layer.
Page 33 of 52
The savings due to aggregate deductibles can be estimated directly from the experience
rating if they are set at a sufficiently low level (say, half of the expected value). A better
approach is the use of an aggregate distribution model. An excess charge factor for a
given AAD is defined as:
where g(y) is the distribution of aggregate losses in the layer
The form of this expression may be recognized as that underlying Table M; it is also
analogous to the ELF calculation used for per occurrence excess. This charge may be
estimated from a number of different methods. These methods are outlined in a
separate section on aggregate distributions.
The charge factor Ï•AAD is multiplied by the loss cost for the layer gross of the AAD to
estimate the net loss cost.
A second type of loss sensitive program is the “swing plan” which is a type of
retrospective rating program. Actual losses to the layer are loaded for expenses and the
result is charged back to the ceding company, subject to maximum and minimum
constraints.
Swing plans likewise require aggregate distribution models to be evaluated correctly. A
swing plan formula may work as follows:
Retro Premium = (Actual Layer Losses) x 100/80
Provisional Rate = 15%
Maximum Premium = 30% x Subject Premium
Minimum Premium = 10% x Subject Premium
For example, if actual losses in the layer are $100,000, then the ultimate premium paid
to the reinsurer will be $125,000, subject to the maximum and minimum.
This formula may apply to a block of years instead of to a single year. Following the
example of sliding scale commissions, the calculation of expected premium is as
follows:
Page 34 of 52
Range of
Loss Cost
Probability
Average
in Range
Loaded
Loss Cost
Capped
Premium
0% < LC < 8% 8% < LC < 24% 24% < LC 0.120 0.630 0.250 6.0% 18.0% 40.0% 7.5% 22.5% 50.0% 10.0% 22.5% 30.0% Total 1.000 22.1% 27.6% 22.9% In this example, the expected loss ratio is 96.5% (= 22.1%/22.9%), not 80% (from the 100/80 loading) because the maximum and minimum amounts are not in "balance". The loading, maximum or minimum rates can be adjusted to produce an acceptable loss ratio. A second issue on the swing plan is that the provisional rate of 15% is well below the expected ultimate swing plan premium rate of 22.9%; this difference is an added cash flow advantage for the ceding company which mu... Purchase answer to see full attachment

  
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