quantile.MackChainLadder function

quantile function for Mack-chain-ladder

quantile methods for a MackChainLadder object

## 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.

Returns

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

References

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

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

Author(s)

Eric Dal Moro eric_dal_moro@yahoo.com

See Also

See also MackChainLadder

Examples

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