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:
Conditionally, given
we have
the random vector
has multivariate Gaussian distribution with uncorrelated components given by
cumulative payments are given by the recursion
with initial value
;
incurred losses
are given by the backwards recursion
with initial value
.
The components of
are independent and
for all j.
Parameters 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
and
and
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:
-
Ult.Loss.Origin Ultimate losses for different origin years.
-
Ult.Loss Total ultimate loss.
-
Res.Origin Claims reserves for different origin years.
-
Res.Tot Total reserve.
-
s.e. Square root of mean square error of prediction for the total ultimate loss.
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)