基础数据:来源于Taylor and Ashe(1983)累计赔款数据,也就是书上的例子,
增量赔款
357,848766,940610,542482,940527,326574,398 352,118884,021933,8941,183,289445,745320,996 290,5071,001,799926,2191,016,654750,816146,923 310,6081,108,250776,1891,562,400272,482352,053 443,160693,190991,983769,488504,851470,639 396,132937,085847,498805,037705,960
440,832847,6311,131,3981,063,269
359,4801,061,6481,443,370
376,686986,608
344,014
累计赔款
357,8481,124,7881,735,3302,218,2702,745,5963,319,994 352,1181,236,1392,170,0333,353,3223,799,0674,120,063 290,5071,292,3062,218,5253,235,1793,985,9954,132,918 310,6081,418,8582,195,0473,757,4474,029,9294,381,982 443,1601,136,3502,128,3332,897,8213,402,6723,873,311 396,1321,333,2172,180,7152,985,7523,691,712
440,8321,288,4632,419,8613,483,130
359,4801,421,1282,864,498
376,6861,363,294
344,014
进展因子:这里采用加权平均数
987654
3.4906 1.7473 1.4574 1.1739 1.1038 1.0863拟合累计赔款数据,由斜线数据除以进展因子,进而计算拟合增量赔款数据
拟合累计赔款
270,061942,6781,647,1722,400,6102,817,9603,110,531 376,1251,312,9042,294,0813,343,4233,924,6824,332,157 372,3251,299,6412,270,9053,309,6473,885,0354,288,393 366,7241,280,0892,236,7413,259,8563,826,5874,223,877 336,2871,173,8462,051,1002,989,3003,508,9953,873,311 353,7981,234,9702,157,9033,144,9563,691,712
391,8421,367,7652,389,9413,483,130
469,6481,639,3552,864,498
390,5611,363,294
344,014
拟合增量赔款
270,061672,617704,494753,438417,350292,571 376,125936,779981,1761,049,342581,260407,474 372,325927,316971,2641,038,741575,388403,358 366,724913,365956,6521,023,114566,731397,290 336,287837,559877,254938,200519,695364,316 353,798881,172922,933987,053546,756
391,842975,9231,022,1751,093,189
469,6481,169,7071,225,143
390,561972,733
344,014
计算残差:使用书中介绍的Pearson残差,r表示残差,C表示真实增量赔款,m表示拟合增量赔款(r=(C-m)/m^0.5)Pearson残差
168.93115.01-111.94-311.63170.23521.04
-39.14-54.51-47.73130.76-177.75-135.47
-134.0977.35-45.71-21.67231.27-403.77
-92.67203.92-184.51533.16-390.87-71.77
184.29-157.75122.49-174.18-20.59176.15
71.1759.56-78.52-183.21215.31
78.26-129.87108.03-28.62
-160.76-99.91197.16
-22.2014.07
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对Person残差有放回的抽样,第一步生成1到总数的随机数,第二步找到该随机数对应的行和列,第三步,找到对应的数NUM
202146465051
49552336129
555549273454
121446332332
443848332149
2135253712
34144147
48143
950
52
ROW
6610101010
10107818
1010107810
5510878
99108610
68795
85910
1019
410
10
COLUMN
561156
4102811
10104669
241524
823564
67412
6452
317
35
7
残差抽样
-20.59176.15168.93168.93170.23521.04 -311.63-0.00203.9258.77--134.09
-0.00-0.00-311.63-71.77-403.77-86.91
59.56-183.21168.93231.27203.92-21.67
25.11-54.51-111.94231.27176.15-311.63
176.15207.21533.16-39.1459.56
-403.77-183.21-177.75115.01
-111.94-252.02
108.03170.23
-235.52
用抽样所得残差与拟合赔款数据,得到抽样的增量赔款以及抽样的累计赔款。
抽样增量赔款
259,360.90817,084.46846,280.88900,066.99527,326.00574,398.00 185,005.03936,779.401,183,166.171,109,539.80581,259.75321,881.17 372,325.32927,315.87664,143.87965,595.12269,112.24348,161.24 402,794.54738,275.291,121,876.641,257,041.72720,244.30383,630.03 350,850.92787,673.00772,412.921,162,209.31646,682.47176,220.37 458,574.811,075,683.811,435,136.34948,162.32590,799.32
139,093.92794,936.76842,468.811,213,438.82
392,937.161,169,707.191,504,099.22
458,074.771,140,630.59
205,877.73
抽样累计赔款
259,360.901,076,445.361,922,726.232,822,793.223,350,119.223,924,517.22 185,005.031,121,784.442,304,950.613,414,490.413,995,750.164,317,631.33 372,325.321,299,641.181,963,785.052,929,380.173,198,492.413,546,653.65 402,794.541,141,069.822,262,946.463,519,988.184,240,232.474,623,862.51 350,850.921,138,523.911,910,936.833,073,146.143,719,828.613,896,048.98 458,574.811,534,258.622,969,394.953,917,557.274,508,356.59
139,093.92934,030.681,776,499.492,989,938.31
392,937.161,562,644.353,066,743.57
458,074.771,598,705.36
205,877.73
用抽样累计赔款计算准备金,第一步进展因子,第二步各个事故年准备金,第三步总体准备金
进展因子:这里采用加权平均数
987654
3.7784 1.8533 1.5000 1.1695 1.0975 1.0760
各事故年准备金
3,169,568.055,338,433.984,113,544.181,676,946.001,508,653.23841,786.72总准备金
17,606,784.81
146,342139,950227,22967,948
527,804266,172425,046
495,992280,405
206,286
3,466,3363,606,2863,833,5153,901,463
4,647,8674,914,0395,339,085
4,628,9104,909,315
4,588,268
321-
1.0539 1.0766 1.0177 1.0000
3,378,8743,560,9093,833,5153,901,463
4,705,8894,959,4165,339,085
4,658,3494,909,315
4,588,268
268,344182,035272,60667,948
373,732253,527379,669
369,957250,966
364,391
-235.52-98.64-86.91-0.00 252.0225.1173.64
207.2158.77
-261.92
55
13251019 314120
5328
55
5746
896
107
10
3444
355
87
10
-78.52533.16-28.62-174.18 -45.71-177.75-20.59
-98.64-261.92
-0.00
227,667.78409,509.83257,664.7222,544.88 345,790.19164,028.75366,981.48
309,960.87119,754.88
364,391.17
4,152,185.004,561,694.834,819,359.554,841,904.44 4,663,421.524,827,450.275,194,431.74
3,856,614.523,976,369.40
4,988,253.68
321-
1.0547 1.0665 1.0047 1.0000
649,172.18284,381.0024,299.47-