permuteReserve {ProfileLadder}R Documentation

Permutation bootstrap reserve (PARALLAX, REACT, MACRAME)

Description

The function takes the output from the function parallelReserve() or mcReserve and estimates the overall reserve distribution in terms of the permutation bootstrap approach proposed in Maciak, Mizera, and Pešta (2022).

Usage

permuteReserve(object, B = 500, std = TRUE, quantile = 0.995)

Arguments

object

an object of the class profileLadder (output from parallelReserve() or mcReserve() respectively)

B

number of permutations to be performed (DEFAULT B = 500)

std

logical to indicate whether the run-off triangle should be standardized by the first column increments (DEFAULT) or not (std = FALSE). For more details about the triangle standardization, see Maciak, Mizera, and Pešta (2022)

quantile

quantile level for the BootVar. characteristic of the bootstrapped distribution (the DEFAULT choice quantile = 0.995 is explicitly required by the Solvency II principle used by actuaries in practice)

Value

An object of the class permutedReserve which is a list with the following elements:

eSummary

numeric vector with four values summarizing the estimated reserve: Paid amount (i.e., the sum of the last observed diagonal in the given cumulative run-off triangle); Estimated ultimate (i.e., the sum of the last column in the completed cumulative triangle); Estimated reserve (i.e., the sum of the last column in the completed cumulative triangle minus the sum of the last observed diagonal); True reserve if a completed (true) run-off triangle is available

pSummary

numeric vector with four values summarizing the overall reserve distribution: Boot.Mean gives the verage of B permutation bootstrap reserves; Std.Er. provides the corresponding standard error of B permutation bootstrap reserves; The value of BootCov% stands for a percentage proportion between the standard error and the average; Finally, BootVar.995 provides the estimated 0.995 quantile (by DEFAULT) of the boostrap reserve distribution (for quantile = 0.995 and, otherwise, it is modified acordingly) given relatively with respect to the permutation bootstrapped mean reserve

pReserves

a numeric vector of the length B with the estimated (permuted) reserves for each row-permuted run-off triangle in B independent Monte Carlo simulation runs

pUltimates

A matrix of the dimensions B x n (where n stands for the number of the origin/development periods) with B simulated ultimate payments – the last column in the completed run-off triangle

pLatest

A matrix of the dimensions B x n (where n again stands for the number of the origin/development periods) with B simulated diagonals

trueComplete

The true complete run-off triangle (if available) and NA value otherwise

info

a numeric vector summarizing the bootstrap compuational efficiency: In particular, the OS/Architecture type, the number of permutations (B), the input run-off triangle dimension (n) and the computation time needed for the permutation bootstrap calculations

References

Maciak, M., Mizera, I., and Pešta, M. (2022). Functional Profile Techniques for Claims Reserving. ASTIN Bulletin, 52(2), 449-482. DOI:10.1017/asb.2022.4

European Parliament and Council (2009). Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II). Official Journal of the European Union, 1–155.
https://data.europa.eu/eli/dir/2009/138/oj

See Also

parallelReserve(), mcReserve(), plot.permutedReserve()

Examples

## REACT algorithm and the permutation bootstrap reserve 
data(CameronMutual)
output <- parallelReserve(CameronMutual, method = "react")
permuteReserve(output, B = 100)

## MACRAME algorithm with a pre-specified number of states 
output <- mcReserve(CameronMutual, states = 5)
permuteReserve(output, B = 100)



[Package ProfileLadder version 0.1.2 Index]