Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account
Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account
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DOI：
10.3390/risks5010011
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
Wenjun Jiang;Jiandong Ren;R. Zitikis
中科院分区：
文献类型：
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作者：
Wenjun Jiang;Jiandong Ren;R. Zitikis
保险精算文献对再保险保单的最优形式进行了长期的研究。大多数现有的结果都是从保险人的角度出发，旨在使预期效用最大化或使保险人的风险最小化。然而，正如Borch（1969）所指出的那样，可以理解的是，对一方（例如，保险人）可能非常有吸引力的再保险安排可能对另一方（例如，再保险人）来说是非常不可接受的。本文遵循这一观点，研究了以风险价值（VaR）衡量的一方风险不能在不增加再保险交易对手VaR的情况下降低的帕累托最优再保险政策的形式。我们证明了再保险交易中双方VaR的线性组合的最小化可以确定帕累托最优策略。因此，我们成功地推导出用户友好的、封闭的、最优的再保险策略及其参数值。
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.