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INDIVIDUAL LOSS RESERVING WITH THE MULTIVARIATE SKEW NORMAL FRAMEWORK

Published online by Cambridge University Press:  06 August 2013

Mathieu Pigeon ,
Katrien Antonio  and
Michel Denuit
Mathieu Pigeon*
Affiliation:
Université Catholique de Louvain, UCL, Belgium
Katrien Antonio
Affiliation:
KU Leuven, Belgium and University of Amsterdam, UvA, The Netherlands E-Mail: [email protected]
Michel Denuit
Affiliation:
Université Catholique de Louvain, UCL, Belgium E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

The evaluation of future cash flows and solvency capital recently gained importance in general insurance. To assist in this process, our paper proposes a novel loss reserving model, designed for individual claims developing in discrete time. We model the occurrence of claims, as well as their reporting delay, the time to the first payment, and the cash flows in the development process. Our approach uses development factors similar to those of the well-known chain–ladder method. We suggest the Multivariate Skew Normal distribution as a multivariate distribution suitable for modeling these development factors. Empirical analysis using a real portfolio and out-of-sample prediction tests demonstrate the relevance of the model proposed.

Keywords

Stochastic loss reservinggeneral insuranceMultivariate Skew Normal distributionchain–ladderindividual claims
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 3 , September 2013 , pp. 399 - 428
Copyright
Copyright © ASTIN Bulletin 2013 

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