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OPTIMAL PROPORTIONAL REINSURANCE UNDER TWO CRITERIA: MAXIMIZING THE EXPECTED UTILITY AND MINIMIZING THE VALUE AT RISK

Part of: Mathematical economics

Published online by Cambridge University Press:  06 January 2011

ZHIBIN LIANG  and
JUNYI GUO
ZHIBIN LIANG*
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, Jiangsu 210046, PR China (email: [email protected])
JUNYI GUO
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We consider the optimal proportional reinsurance from an insurer’s point of view to maximize the expected utility and minimize the value at risk. Under the general premium principle, we prove the existence and uniqueness of the optimal strategies and Pareto optimal solution, and give the relationship between the optimal strategies. Furthermore, we study the optimization problem with the variance premium principle. When the total claim sizes are normally distributed, explicit expressions for the optimal strategies and Pareto optimal solution are obtained. Finally, some numerical examples are presented to show the impact of the major model parameters on the optimal results.

Keywords

proportional reinsuranceexpected utilityvalue at riskpremium principlePareto optimal solution

MSC classification

Secondary: 91B30: Risk theory, insurance
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 4 , April 2010 , pp. 449 - 463
Copyright
Copyright © Australian Mathematical Society 2010

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