PaidIncurredChain {ChainLadder}R Documentation

PaidIncurredChain

Description

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

Usage

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] distributed as N(φ[m],s^2[m]),

Ψ[n] distributed as 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

PaidIncurredChain(USAApaid, USAAincurred)

[Package ChainLadder version 0.2.14 Index]