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Bootstrapping示例

Bootstrapping示例
Bootstrapping示例

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

-

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-

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