quantile.MackChainLadder {ChainLadder}

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))