PaidIncurredChain: PaidIncurredChain

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

View source: R/PIC.R

Description

The Paid-incurred Chain model (Merz, Wuthrich (2010)) combines claims payments and incurred losses information to get a unified ultimate loss prediction.

Usage

1
PaidIncurredChain(triangleP, triangleI)

Arguments

triangleP

Cumulative claims payments triangle

triangleI

Incurred losses triangle.

Details

The method uses some basic properties of multivariate Gaussian distributions to obtain a mathematically rigorous and consistent model for the combination of the two information channels.

We assume as usual that I=J. The model assumptions for the Log-Normal PIC Model are the following:

Parameters Θ in the model are in general not known and need to be estimated from observations. They are estimated in a Bayesian framework. In the Bayesian PIC model they assume that the previous assumptions hold true with deterministic σ_0,...,σ_J and τ_0,...,τ_{J-1} and

Φ_m \sim N(φ_m,s^2_m),

Ψ_n \sim N(ψ_n,t^2_n).

This is not a full Bayesian approach but has the advantage to give analytical expressions for the posterior distributions and the prediction uncertainty.

Value

The function returns:

Note

The model is implemented in the special case of non-informative priors.

Author(s)

Fabio Concina, fabio.concina@gmail.com

References

Merz, M., Wuthrich, M. (2010). Paid-incurred chain claims reserving method. Insurance: Mathematics and Economics, 46(3), 568-579.

See Also

MackChainLadder,MunichChainLadder

Examples

1

ChainLadder documentation built on May 29, 2017, 2:08 p.m.