Summary Method for the S3 Objects permutedReserve
summary.permutedReserve.RdThe function provides an overall summary of the output from the function
permuteReserve() (i.e., the summary of the object of the class
permutedReserve)
Usage
# S3 method for class 'permutedReserve'
summary(object, triangle.summary = FALSE, ...)Arguments
- object
an object of the class
permutedReserve– i.e., the output form thepermuteReserve()functions- triangle.summary
logical (
FALSEby DEFAULT) indicating whether a brief table with the empirical summary of the permutted run-off triangles (the first column, the last running diagonal, and the ultimate amounts in particular) should be printed in the output or not- ...
not used
Value
Summary of the completed functional profiles (provided by one of the
functions parallelReserve() or mcReserve()) and the overall
reserve distribution obtained in terms of the permutation bootstrap – the
function permuteReserve().
The output is a list with the following items:
- origins
a matrix with the row-specific summary of the completed functional profiles (except the first fully developed profile—i.e., the first row in the run-off triangle). The first column of the matrix (
First) gives the first origin payments; The second column (Latest) gives the last available (cumulative) payments (i.e., values from the last running diagonal in the run-off triangle); The third column (Dev.To.Date) gives a relative proportion of the paid amount (Latest) with respect to the estimated ultimate (Ultimate) given in the fourth column; The column denoted asIBNRgives the estimated amount still left to pay (Incurred But Not Reported); The sixth column provides the estimated standard errors (S.E.) of IBNR obtained from the permutation bootstrap; The last column returns the corresponding coefficients of variation (CV).- overall
Table with the summary of the true/estimated reserve:
Paid amountrepresents the sum of the last running diagonal;Estimated reservegives the reserve estimate provided by one of the estimation algorithm (PARALLAX, REACT, or MACRAME);True reserveis given as a sum of the last column (if available,NAotherwise); Finally, some Accuracy in terms ofReserve%is given as a percentage of the estimated reserve with respect to the true reserve (see Maciak, Mizera, and Pešta (2022) andDev.To.Dategives the proportion of the overall estimatd ultimate and the overall paid amount- dist
Table with basic empirical characteristics of the overall reserve distribution provided by the permutation bootstrap:
Boot.Meanstands for the empirical mean of the bootstrap distribution;Std.Er.gives the corresponding standard error of the bootstrap distribution;BootCov%stands for a percentage proportion between the standard error and the empirical mean of the bootstrap distribution; Finally,BootVar.xxxprovides the estimated quantile of the bootstrap reserve distribution (0.995 by DEFAULT).
Examples
data(CameronMutual)
summary(CameronMutual)
#> 1 2 3 4 5
#> Min. :3689 Min. : 6043 Min. : 6789 Min. : 7089 Min. : 7164
#> 1st Qu.:5066 1st Qu.: 8055 1st Qu.: 8978 1st Qu.: 9402 1st Qu.: 9776
#> Median :5186 Median : 8590 Median : 9551 Median :10189 Median :10618
#> Mean :5448 Mean : 8866 Mean :10105 Mean :10669 Mean :11009
#> 3rd Qu.:5926 3rd Qu.: 9761 3rd Qu.:11500 3rd Qu.:12098 3rd Qu.:12507
#> Max. :7452 Max. :12421 Max. :14171 Max. :14752 Max. :15066
#> 6 7 8 9
#> Min. : 7197 Min. : 7253 Min. : 7267 Min. : 7266
#> 1st Qu.: 9854 1st Qu.: 9908 1st Qu.: 9959 1st Qu.: 9908
#> Median :10724 Median :10758 Median :10792 Median :10792
#> Mean :11158 Mean :11241 Mean :11289 Mean :11294
#> 3rd Qu.:12702 3rd Qu.:12806 3rd Qu.:12882 3rd Qu.:12888
#> Max. :15354 Max. :15637 Max. :15720 Max. :15744
#> 10
#> Min. : 7266
#> 1st Qu.: 9907
#> Median :10803
#> Mean :11312
#> 3rd Qu.:12890
#> Max. :15786
## summary for the point reserve prediction
summary(parallelReserve(CameronMutual))
#> PARALLAX reserve prediction (by origins)
#> First Latest Dev.To.Date Ultimate IBNR
#> 2 5984 13113 1.0000000 13113 0
#> 3 7452 15720 0.9997456 15724 4
#> 4 7115 13872 0.9943373 13951 79
#> 5 5753 11282 0.9883487 11415 133
#> 6 3937 8757 0.9690163 9037 280
#> 7 5127 9325 0.9496894 9819 494
#> 8 5046 8984 0.9142159 9827 843
#> 9 5129 8202 0.8361709 9809 1607
#> 10 3689 3689 0.4197292 8789 5100
#> total 49232 92944 0.9158488 101484 8540
#>
#> Overall reserve summary
#> Est.Reserve Est.Ultimate Paid Amount True Reserve Reserve%
#> 8540.00 113699.00 105159.00 7963.00 7.25
#>
## summary for the overall reserve distribution
summary(permuteReserve(parallelReserve(CameronMutual)))
#>
| | 0 % ~calculating
|> | 1 % ~01s
|> | 2 % ~01s
|>> | 3 % ~01s
|>> | 4 % ~01s
|>>> | 5 % ~01s
|>>> | 6 % ~01s
|>>>> | 7 % ~01s
|>>>> | 8 % ~01s
|>>>> | 9 % ~01s
|>>>>> | 10% ~01s
|>>>>> | 11% ~01s
|>>>>>> | 12% ~01s
|>>>>>> | 13% ~01s
|>>>>>>> | 14% ~01s
|>>>>>>> | 15% ~01s
|>>>>>>> | 16% ~01s
|>>>>>>>> | 17% ~01s
|>>>>>>>> | 18% ~01s
|>>>>>>>>> | 19% ~01s
|>>>>>>>>> | 20% ~01s
|>>>>>>>>>> | 21% ~01s
|>>>>>>>>>> | 22% ~01s
|>>>>>>>>>> | 23% ~01s
|>>>>>>>>>>> | 24% ~01s
|>>>>>>>>>>> | 25% ~01s
|>>>>>>>>>>>> | 26% ~01s
|>>>>>>>>>>>> | 27% ~01s
|>>>>>>>>>>>>> | 28% ~01s
|>>>>>>>>>>>>> | 29% ~01s
|>>>>>>>>>>>>> | 30% ~01s
|>>>>>>>>>>>>>> | 31% ~01s
|>>>>>>>>>>>>>> | 32% ~01s
|>>>>>>>>>>>>>>> | 33% ~01s
|>>>>>>>>>>>>>>> | 34% ~01s
|>>>>>>>>>>>>>>>> | 35% ~01s
|>>>>>>>>>>>>>>>> | 36% ~01s
|>>>>>>>>>>>>>>>> | 37% ~01s
|>>>>>>>>>>>>>>>>> | 38% ~01s
|>>>>>>>>>>>>>>>>> | 39% ~01s
|>>>>>>>>>>>>>>>>>> | 40% ~01s
|>>>>>>>>>>>>>>>>>> | 41% ~01s
|>>>>>>>>>>>>>>>>>>> | 42% ~01s
|>>>>>>>>>>>>>>>>>>> | 43% ~01s
|>>>>>>>>>>>>>>>>>>> | 44% ~01s
|>>>>>>>>>>>>>>>>>>>> | 45% ~01s
|>>>>>>>>>>>>>>>>>>>> | 46% ~01s
|>>>>>>>>>>>>>>>>>>>>> | 47% ~00s
|>>>>>>>>>>>>>>>>>>>>> | 48% ~00s
|>>>>>>>>>>>>>>>>>>>>>> | 49% ~00s
|>>>>>>>>>>>>>>>>>>>>>> | 50% ~00s
|>>>>>>>>>>>>>>>>>>>>>> | 51% ~00s
|>>>>>>>>>>>>>>>>>>>>>>> | 52% ~00s
|>>>>>>>>>>>>>>>>>>>>>>> | 53% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>> | 54% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>> | 55% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>> | 56% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>> | 57% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>> | 58% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>> | 59% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>> | 60% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>> | 61% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>> | 62% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 63% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 64% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 65% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 66% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 67% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 68% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 69% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 70% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 71% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 72% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 73% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 74% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 75% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 76% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 77% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 78% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 79% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 80% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 81% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 82% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 83% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 84% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 85% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 86% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 87% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 88% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 89% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 90% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 91% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 92% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 93% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 94% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 95% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 96% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> | 97% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>| 98% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>| 99% ~00s
|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>| 100% elapsed=01s
#> PARALLAX based reserve prediction (with B = 500 bootstrap permutations)
#> First Latest Dev.To.Date Ultimate IBNR S.E CV
#> 2 5984 13113 1.0000000 13113 0 0.000000 NaN
#> 3 7452 15720 0.9997456 15724 4 8.112413 2.0281032
#> 4 7115 13872 0.9943373 13951 79 25.757557 0.3260450
#> 5 5753 11282 0.9883487 11415 133 58.295361 0.4383110
#> 6 3937 8757 0.9690163 9037 280 68.777973 0.2456356
#> 7 5127 9325 0.9496894 9819 494 98.820026 0.2000405
#> 8 5046 8984 0.9142159 9827 843 223.150265 0.2647097
#> 9 5129 8202 0.8361709 9809 1607 558.250631 0.3473868
#> 10 3689 3689 0.4197292 8789 5100 647.832695 0.1270260
#> total 49232 92944 0.9158488 101484 8540 877.800532 0.1027869
#>
#> Overall reserve distribution
#> Boot.Mean Std.Er. BootCov% BootVar.995
#> 9057.485652 877.800532 9.691437 1.262077
#>
#> The PARALLAX predicted reserve represents the 30.74% quantile of the reserve distribution
#> Bootstrap simulated reserves beyond 2σ rule: 17 (out of 500)
#>