quantile.MackChainLadder: quantile function for Mack-chain-ladder

In ChainLadder: Statistical Methods and Models for Claims Reserving in General Insurance

quantile function for Mack-chain-ladder

Description

quantile methods for a MackChainLadder object

Usage

## S3 method for class 'MackChainLadder'
quantile(x, probs=c(0.75, 0.95), na.rm = FALSE,
              names = TRUE, type = 7,...)

Arguments

x	object of class "MackChainLadder"
probs	numeric vector of probabilities with values in [0,1], see quantile for more help
na.rm	not used
names	not used
type	not used
...	not used

Details

Reserves at the desired quantile using the Cornish-Fisher expansion.

The Cornish-Fisher expansion relies on the first three moments of the reserve risk distribution: The Best estimate resulting from the Chain-Ladder projection, the Mack standard deviation and the skewness of the distribution (for skewness estimation, see references below).

The quantile estimation requires only that the standard Mack assumptions are met.

For details of the underlying calculations, see references below.

Value

quantile.MackChainLadder gives a list with two elements back:

ByOrigin	data frame with skewness and quantile statistics by origin period
Totals	data frame with total skewness and quantile statistics across all origin periods

Author(s)

Eric Dal Moro [e-mail]

References

Eric Dal Moro and Yuriy Krvavych. Probability of sufficiency of Solvency II Reserve risk margins: Practical approximations. ASTIN Bulletin, 47(3), 737-785

Dal Moro, Eric, A Closed-Form Formula for the Skewness Estimation of Non-Life Reserve Risk Distribution (September 15, 2013). Available at SSRN: https://ssrn.com/abstract=2344297 or https://dx.doi.org/10.2139/ssrn.2344297

See Also

See also MackChainLadder

Examples

M <- MackChainLadder(GenIns, est.sigma="Mack")
quantile(M, c(0.65, 0.75, 0.9))

ChainLadder documentation built on Sept. 11, 2024, 8:35 p.m.