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Optimal Reinsurance Revisited – A Geometric Approach

Published online by Cambridge University Press:  09 August 2013

Ka Chun Cheung
Ka Chun Cheung*
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, Tel.: +852-28591987, Fax: +852-28589041, E-Mail: kccg@hku.hk
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Abstract

In this paper, we reexamine the two optimal reinsurance problems studied in Cai et al. (2008), in which the objectives are to find the optimal reinsurance contracts that minimize the value-at-risk (VaR) and the conditional tail expectation (CTE) of the total risk exposure under the expectation premium principle. We provide a simpler and more transparent approach to solve these problems by using intuitive geometric arguments. The usefulness of this approach is further demonstrated by solving the VaR-minimization problem when the expectation premium principle is replaced by Wang's premium principle.

Keywords

Value-at-riskconditional tail expectationreinsuranceexpectation premium principlecomonotonicityWang's premium principleincreasing convex function
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 221 - 239
Copyright
Copyright © International Actuarial Association 2010

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