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Estimating Copulas for Insurance from Scarce Observations, Expert Opinion and Prior Information: A Bayesian Approach

Published online by Cambridge University Press:  09 August 2013

Philipp Arbenz  and
Davide Canestraro
Davide Canestraro
Affiliation:
SCOR SE, Zurich Branch, General Guisan – Quai 26, CH-8022 Zürich, Switzerland, E-mail: dcanestraro@scor.com
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Abstract

A prudent assessment of dependence is crucial in many stochastic models for insurance risks. Copulas have become popular to model such dependencies. However, estimation procedures for copulas often lead to large parameter uncertainty when observations are scarce. In this paper, we propose a Bayesian method which combines prior information (e.g. from regulators), observations and expert opinion in order to estimate copula parameters and determine the estimation uncertainty. The combination of different sources of information can significantly reduce the parameter uncertainty compared to the use of only one source. The model can also account for uncertainty in the marginal distributions. Furthermore, we describe the methodology for obtaining expert opinion and explain involved psychological effects and popular fallacies. We exemplify the approach in a case study.

Keywords

CopulasExpert judgmentInsuranceDependence measureBayesian inferenceCorrelationRisk management
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 1 , May 2012 , pp. 271 - 290
Copyright
Copyright © International Actuarial Association 2012

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