Summary Method for the S3 Objects permutedReserve
Source: R/summary.permutedReserve.R
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% ~00s
|>>>>>>>>>>>>>>>>>>>>> | 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)
#>