Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/MackChainLadderFunctions.R

`quantile`

methods for a `MackChainLadder`

object

1 2 3 |

`x` |
object of class |

`probs` |
numeric vector of probabilities with values in [0,1],
see |

`na.rm` |
not used |

`names` |
not used |

`type` |
not used |

`...` |
not used |

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.

`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 |

Eric Dal Moro eric_dal_moro@yahoo.com

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 `MackChainLadder`

1 2 | ```
M <- MackChainLadder(GenIns, est.sigma="Mack")
quantile(M, c(0.65, 0.75, 0.9))
``` |

```
Welcome to ChainLadder version 0.2.7
Type vignette('ChainLadder', package='ChainLadder') to access
the overall package documentation.
See demo(package='ChainLadder') for a list of demos.
More information is available on the ChainLadder project web-site:
https://github.com/mages/ChainLadder
To suppress this message use:
suppressPackageStartupMessages(library(ChainLadder))
$ByOrigin
Skewness IBNR 65% IBNR 75% IBNR 90%
1 0.0000000000 NaN NaN NaN
2 0.0000000000 123739.0 145581.4 191435.9
3 -0.0286634126 516899.3 551912.6 625100.8
4 -0.0432877277 761917.4 800240.3 880168.6
5 -0.0006540419 1085638.2 1161220.1 1319876.2
6 0.1799508151 1567333.2 1689962.3 1954108.1
7 0.0549677343 2388416.0 2551431.7 2896438.1
8 0.2674116868 4224362.7 4489436.4 5067138.8
9 0.2861886611 4613768.9 4908824.4 5553448.6
10 0.3141065593 5090294.9 5506347.5 6418605.5
$Totals
Totals
Skewness 2.142952e-01
IBNR 65%: 1.954935e+07
IBNR 75%: 2.028376e+07
IBNR 90%: 2.187308e+07
```

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