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A COPULA REGRESSION FOR MODELING MULTIVARIATE LOSS TRIANGLES AND QUANTIFYING RESERVING VARIABILITY

Published online by Cambridge University Press:  08 October 2013

Peng Shi
Peng Shi*
Affiliation:
Actuarial Science, Risk Management, and Insurance Department, Wisconsin School of Business, University of Wisconsin–Madison, 975 University Avenue, Madison, Wisconsin 53706, USA E-Mail: pshi@bus.wisc.edu
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Abstract

This article proposes a claims reserving model for dependent lines of business with the accommodation of association among triangles by a copula function. We show that the family of elliptical copulas is a pretty convenient choice to capture the dependencies introduced by various sources, including the common calendar year effects. To quantify the associated reserving variability, we resort to parametric bootstrapping techniques for simulating the predictive distribution of outstanding liabilities and for calculating the three components of predictive uncertainty: the model error, the process error and the estimation error. Numerical analysis is performed for a portfolio of casualty insurance from a major U.S. insurer.

Keywords

Dependent loss reservingcopulacalendar year effectspredictive uncertainty
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 1 , January 2014 , pp. 85 - 102
Copyright
Copyright © ASTIN Bulletin 2013 

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