On Pareto-optimal reinsurance with constraints under distortion risk measures
On Pareto-optimal reinsurance with constraints under distortion risk measures
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DOI：
10.1007/s13385-017-0163-1
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发表时间：
2017-12
影响因子：
1.2
通讯作者：
Wenjun Jiang;Hanping Hong;Jiandong Ren
中科院分区：
文献类型：
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作者：
Wenjun Jiang;Hanping Hong;Jiandong Ren
本文研究帕累托最优再保险政策，其中考虑了保险公司和再保险公司的风险和回报。我们假设保险人和再保险人的风险以及再保险保费是由具有不同扭曲算子的一些扭曲风险度量决定的。在只有当各方的最终风险低于某个预定值时再保险政策才可行的约束下，我们推导出最优再保险政策的显式表达式。在方法论上，我们表明可以利用广义内曼-皮尔逊方法、拉格朗日乘子方法和动态控制方法来解决我们的问题。详细研究了用风险价值（VaR）和尾部风险价值（TVaR）衡量双方风险的特殊情况。提供数值示例来说明结果的实际含义。
This paper studies the Pareto-optimal reinsurance policies, where both the insurer’s and the reinsurer’s risks and returns are considered. We assume that the risks of the insurer and the reinsurer, as well as the reinsurance premium, are determined by some distortion risk measures with different distortion operators. Under the constraint that a reinsurance policy is feasible only if the resulting risk of each party is below some pre-determined values, we derive explicit expressions for the optimal reinsurance polices. Methodologically, we show that the generalized Neyman-Pearson method, the Lagrange multiplier method, and the dynamic control methods can be utilized to solve our problem. Special cases when both parties’ risks are measured by Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are studied in great details. Numerical examples are provided to illustrate practical implications of the results.