Average Premium Per Policy in Group B 260
Number of Policies Sold in Group B 6500

Loss Frequency Data for Group B

Claims Per Policy Per Year Number Policies
0 824 0.824 0
1 153 0.153 0.153
2 23 0.023 0.046
3 0 0 0
TOTAL 1000

Average Frequency per Policy 0.20

Historical Loss Severity Data for Group B

Observation 1 1418
Observation 2 995
Observation 3 1804
Observation 4 1463
Observation 5 1402
Observation 6 1192
Observation 7 1521
Observation 8 796
Observation 9 1800
Observation 10 1137
Observation 11 785
Observation 12 1094
Observation 13 1275
Observation 14 1246
Observation 15 1553
Observation 16 1698
Observation 17 1589
Observation 18 1212
Observation 19 1273
Observation 20 1178
Observation 21 1037
Observation 22 845
Observation 23 886
Observation 24 946
Observation 25 752
Observation 26 1211
Observation 27 1574
Observation 28 2000
Observation 29 870
Observation 30 1285
Observation 31 766
Observation 32 1121
Observation 33 1295
Observation 34 1824
Observation 35 1822
Observation 36 736
Observation 37 1241
Observation 38 1369
Observation 39 1067
Observation 40 1105
Observation 41 1595
Observation 42 1046
Observation 43 1445
Observation 44 1380
Observation 45 950
Observation 46 2169
Observation 47 1921
Observation 48 1018
Observation 49 1657
Observation 50 1368
Observation 51 1068
Observation 52 1197
Observation 53 738
Observation 54 1776
Observation 55 1050
Observation 56 870
Observation 57 1002
Observation 58 894
Observation 59 844
Observation 60 2125
Observation 61 856
Observation 62 1077
Observation 63 1242
Observation 64 1159
Observation 65 814
Observation 66 969
Observation 67 3024
Observation 68 1360
Observation 69 1299
Observation 70 1099
Observation 71 1331
Observation 72 2275
Observation 73 1178
Observation 74 1064
Observation 75 1186
Observation 76 1485
Observation 77 808
Observation 78 1287
Observation 79 1839
Observation 80 1057
Observation 81 971
Observation 82 1017
Observation 83 2444
Observation 84 1775
Observation 85 1054
Observation 86 849
Observation 87 1074
Observation 88 1207
Observation 89 1192
Observation 90 1488
Observation 91 723
Observation 92 1295
Observation 93 1075
Observation 94 2019
Observation 95 1262
Observation 96 1136
Observation 97 1170
Observation 98 1244
Observation 99 911
Observation 100 1421
Observation 101 1708
Observation 102 863
Observation 103 1453
Observation 104 1130
Observation 105 1931
Observation 106 766
Observation 107 936
Observation 108 988
Observation 109 1903
Observation 110 1029
Observation 111 2160
Observation 112 684
Observation 113 807
Observation 114 1836
Observation 115 1248
Observation 116 1378
Observation 117 1688
Observation 118 981
Observation 119 929
Observation 120 1592
Observation 121 1059
Observation 122 1451
Observation 123 710
Observation 124 1188
Observation 125 1566
Observation 126 1085
Observation 127 975
Observation 128 1538
Observation 129 1941
Observation 130 1127
Observation 131 1552
Observation 132 1297
Observation 133 1048
Observation 134 1369
Observation 135 1154
Observation 136 803
Observation 137 1237
Observation 138 1044
Observation 139 1427
Observation 140 1522
Observation 141 2025
Observation 142 1082
Observation 143 1021
Observation 144 1813
Observation 145 782
Observation 146 1640
Observation 147 1011
Observation 148 980
Observation 149 1262
Observation 150 2216
Observation 151 1079
Observation 152 1721
Observation 153 1620
Observation 154 1437
Observation 155 1011
Observation 156 1612
Observation 157 909
Observation 158 1965
Observation 159 1153
Observation 160 1322
Observation 161 997
Observation 162 807
Observation 163 1244
Observation 164 1425
Observation 165 1131
Observation 166 1745
Observation 167 911
Observation 168 1382
Observation 169 1355
Observation 170 1421
Observation 171 1148
Observation 172 1442
Observation 173 1774
Observation 174 1094
Observation 175 1090
Observation 176 1218
Observation 177 1446
Observation 178 1610
Observation 179 1012
Observation 180 1255
Observation 181 717
Observation 182 1622
Observation 183 1054
Observation 184 1762
Observation 185 1255
Observation 186 2222
Observation 187 1276
Observation 188 861
Observation 189 816
Observation 190 1883
Observation 191 1057
Observation 192 1066
Observation 193 1267
Observation 194 1366
Observation 195 791
Observation 196 1319
Observation 197 872
Observation 198 895
Observation 199 1215
Observation 200 1191
Observation 201 805
Observation 202 1226
Observation 203 999
Observation 204 1856
Observation 205 986
Observation 206 947
Observation 207 1386
Observation 208 1381
Observation 209 1590
Observation 210 1939
Observation 211 1213
Observation 212 998
Observation 213 1426
Observation 214 745
Observation 215 2046
Observation 216 1113
Observation 217 1303
Observation 218 1018
Observation 219 1984
Observation 220 1726
Observation 221 798
Observation 222 1352
Observation 223 720
Observation 224 894
Observation 225 702
Observation 226 1145
Observation 227 2046
Observation 228 1209
Observation 229 1225
Observation 230 1264
Observation 231 1629
Observation 232 1245
Observation 233 818
Observation 234 1913
Observation 235 1761
Observation 236 1106
Observation 237 1535
Observation 238 1708
Observation 239 1808
Observation 240 1533
Observation 241 978
Observation 242 1320
Observation 243 885
Observation 244 1247
Observation 245 1011
Observation 246 1393
Observation 247 1555
Observation 248 1677
Observation 249 1185
Observation 250 1356
Write up guide part B.

The general structure of your report should be as follows: the inputs for your calculation (statistics), the method and code you used to derive your answer (you should copy and paste the code you use in your write up) and try to discuss how it works, the results from your model or calculation, trying to interpret your results. You SHOULD NOT paste 10000s of simulated values into your write up.

Breaking this down into the sections:

Question 2A and 2B, discuss the idea of the Empirical CDF and then discuss how you fit the Pareto and Gamma distribution to the dataset. You need to copy and paste your Pareto and Gamma code into your write up and discuss how these functions work perhaps relating them to equations from the class. You need display the graphs and comment on which distribution you decide provides the best fit.

Question 2C,. you should discuss the frequency severity model and the idea of simulation or generating random variables from distributions. Discuss how you will use the Poisson distribution for the frequency and discuss how you calculate the average frequency for each group of policies. Discuss the idea of estimating the Aggregate loss from the sum of individual losses. You need to paste the code you use and try to explain how it works. Discuss how you can calculate the aggregate loss over both groups if they are independent.

Does the Central Limit Theorem suggest that the Aggregate Claims Distribution (gamma and Pareto) is Normal?

Question 2D: Discuss how you can estimate the aggregate loss distribution using the output from your simulation in 2C and produce a graph of the result. You need to discuss how you could estimate the PML from this or the probability of observing a loss greater than a given value.

Question 2E: Discuss how you can also use the simulation to estimate the distributions of profits, and again graph your results . Discuss how you calculate the probability of making a loss.

Question 2F: Discuss how you could use your Profit Distribution to calculate the SCR. Try to link this to your diagram of the profit distribution.

Question 3: Discuss how you can derive the mean and variance of the aggregate claim for group A and group B by simply using equations and statistics. You need to discuss why you should use the Theoretical Pareto Variance rather than the variance from the losses for Group A and relate this to the equations provided. You need to say how you can derive the mean and variance Aggregate Claim across both Group A and Group B, and the assumptions behind this. You need to say how you can derive the Mean and the variance of the underwriting profit. You should then discuss why it might be reasonable to assume that the distribution of profits might be Normal and how you could use this to make the required calculations, perhaps using graphs of the CDF if possible. Finally you should compare your answers using the Normal Approximation and your Monte Carlo Simulation and see if there is any difference, and if possible explain the reason for any difference or similarity in the results.