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Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account

Wenjun Jiang (), Jiandong Ren () and Ričardas Zitikis ()
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Wenjun Jiang: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
Jiandong Ren: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
Ričardas Zitikis: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada

Risks, 2017, vol. 5, issue 1, 1-22

Abstract: Optimal forms of reinsurance policies have been studied for a long time in the actuarial literature. Most existing results are from the insurer’s point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement that might be very attractive to one party (e.g., the insurer) can be quite unacceptable to the other party (e.g., the reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party’s risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaR s of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values.

Keywords: optimal reinsurance treaties; value at risk; Pareto optimality (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 M2 M4 K2 (search for similar items in EconPapers)
Date: 2017
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