Optimal proportional reinsurance under two criteria: maximizing the expected utility and minimizing the value at risk

Zhibin Liang, Junyi Guo

Abstract


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.

doi:10.1017/S1446181110000878

Keywords


proportional reinsurance; expected utility; value at risk; premium principle; Pareto optimal solution



DOI: http://dx.doi.org/10.21914/anziamj.v51i0.3181



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.