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Average Value-at-Risk Minimizing Reinsurance Under Wang's Premium Principle with Constraints

Published online by Cambridge University Press:  09 August 2013

K.C. Cheung ,
F. Liu  and
S.C.P. Yam
F. Liu
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, N2L 3G1, Canada
S.C.P. Yam
Affiliation:
Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
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Abstract

In the present work, we study the optimal reinsurance decision problem in which the Average Value-at-Risk of the retained loss is minimized under Wang's premium principle and is also subject to either (1) a budget constraint on reinsurance premium, or (2) a reinsurer's probabilistic benchmark constraint of his potential loss. We show that the optimal reinsurance is a single-insurance layer under Constraint (1), and a cap insurance or a double-insurance layer under Constraint (2); moreover, under Constraint (2), we further establish that under most common circumstances (see Remark after Theorem 3), a cap insurance will suffice to be optimal. Finally, some numerical illustrations will be provided.

Keywords

Optimal reinsuranceAverage Value-at-RiskValue-at-RiskWang's premium principleSingle and double insurance layers
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 2 , November 2012 , pp. 575 - 600
Copyright
Copyright © International Actuarial Association 2012

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