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OPTIMAL REINSURANCE WITH LIMITED CEDED RISK: A STOCHASTIC DOMINANCE APPROACH

Published online by Cambridge University Press:  19 November 2013

Yichun Chi  and
X. Sheldon Lin
Yichun Chi*
Affiliation:
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, China, 100081
X. Sheldon Lin
Affiliation:
Department of Statistical Sciences, University of Toronto, Toronto, Ontario, CanadaM5S 3G3 E-Mail: sheldon@utstat.utoronto.ca
*
E-Mail: yichun_1982@hotmail.com
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Abstract

An optimal reinsurance problem from the perspective of an insurer is studied in this paper, where an upper limit is imposed on a reinsurer's expected loss over a prescribed level. In order to reduce the moral hazard, we assume that both the insurer and the reinsurer are obligated to pay more as the amount of loss increases in a typical reinsurance treaty. We further assume that the optimization criterion preserves the convex order. Such a criterion is very general as most of the criteria for optimal reinsurance problems in the literature preserve the convex order. When the reinsurance premium is calculated as a function of the actuarial value of coverage, we show via a stochastic dominance approach that any admissible reinsurance policy is dominated by a stop-loss reinsurance or a two-layer reinsurance, depending upon the amount of the reinsurance premium. Moreover, we obtain a similar result to Mossin's Theorem and find that it is optimal for the insurer to cede a loss as much as possible under the net premium principle. To further examine the reinsurance premium for the optimal piecewise linear reinsurance policy, we assume the expected value premium principle and derive the optimal reinsurance explicitly under (1) the criterion of minimizing the variance of the insurer's risk exposure, and (2) the criterion of minimizing the risk-adjusted value of the insurer's liability where the liability valuation is carried out using the cost-of-capital approach based on the conditional value at risk.

Keywords

Conditional value at riskconvex ordercost of capitalMossin's Theoremstop-loss reinsurancetwo-layer reinsurance
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 1 , January 2014 , pp. 103 - 126
Copyright
Copyright © ASTIN Bulletin 2013 

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