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Higher Moments of the Claims Development Result in General Insurance

Published online by Cambridge University Press:  09 August 2013

Robert Salzmann ,
Mario V. Wüthrich  and
Michael Merz
Robert Salzmann
Affiliation:
ETH Zurich, RiskLab Switzerland, Department of Mathematics, 8092 Zurich, Switzerland
Mario V. Wüthrich
Affiliation:
ETH Zurich, RiskLab Switzerland, Department of Mathematics, 8092 Zurich, Switzerland
Michael Merz
Affiliation:
University of Hamburg, Department of Business Administration, 20146 Hamburg, Germany
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Abstract

The claims development result (CDR) is one of the major risk drivers in the profit and loss statement of a general insurance company. Therefore, the CDR has become a central object of interest under new solvency regulation. In current practice, simple methods based on the first two moments of the CDR are implemented to find a proxy for the distribution of the CDR. Such approximations based on the first two moments are rather rough and may fail to appropriately describe the shape of the distribution of the CDR. In this paper we provide an analysis of higher moments of the CDR. Within a Bayes chain ladder framework we consider two different models for which it is possible to derive analytical solutions for the higher moments of the CDR. Based on higher moments we can e.g. calculate the skewness and the excess kurtosis of the distribution of the CDR and obtain refined approximations. Moreover, a case study investigates and answers questions raised in IASB.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 1 , May 2012 , pp. 355 - 384
Copyright
Copyright © International Actuarial Association 2012

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