Optimal Reinsurance from the Perspectives of both an Insurer and a Reinsurer
Optimal Reinsurance from the Perspectives of both an Insurer and a Reinsurer
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DOI：
10.1017/asb.2015.23
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Jun Cai;C. Lemieux;Fangda Liu
中科院分区：
文献类型：
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作者：
Jun Cai;C. Lemieux;Fangda Liu
从保险人的角度或从再保险人的角度来看，最优再保险已经在文献中进行了广泛的研究。但是，作为再保险合同的双方当事人，保险人和再保险人之间存在利益冲突。从一方的角度来看，最佳的再保险形式可能不被另一方所接受。本文分别从保险人和再保险人的角度研究最优再保险设计，同时考虑再保险合同设计中保险人的目标和再保险人的目标。我们开发了最优再保险合同，分别在两种类型的约束下，使保险公司损失和再保险公司损失的风险价值（VaR）风险度量的凸组合最小化。约束条件描述了保险人和再保险人双方的利益。在第一种约束条件下，保险人和再保险人各自对自身损失的风险价值都有限制。对于第二种类型的约束，保险人对其损失的风险价值有一个限制，而再保险人对其出售再保险合同的利润有一个目标。对于这两类约束，我们推导出了在期望值再保险保费原则下的广泛再保险保单类别下的最优再保险形式。这些最优再保险形式比仅从一方角度考虑的最优再保险合同更为复杂。所提出的模型也可以简化为在保险人和再保险人双方利益的约束下，使一方损失的风险价值最小化的问题。
Optimal reinsurance from an insurer's point of view or from a reinsurer's point of view has been studied extensively in the literature. However, as two parties of a reinsurance contract, an insurer and a reinsurer have conflicting interests. An optimal form of reinsurance from one party's point of view may be not acceptable to the other party. In this paper, we study optimal reinsurance designs from the perspectives of both an insurer and a reinsurer and take into account both an insurer's aims and a reinsurer's goals in reinsurance contract designs. We develop optimal reinsurance contracts that minimize the convex combination of the Value-at-Risk (VaR) risk measures of the insurer's loss and the reinsurer's loss under two types of constraints, respectively. The constraints describe the interests of both the insurer and the reinsurer. With the first type of constraints, the insurer and the reinsurer each have their limit on the VaR of their own loss. With the second type of constraints, the insurer has a limit on the VaR of his loss while the reinsurer has a target on his profit from selling a reinsurance contract. For both types of constraints, we derive the optimal reinsurance forms in a wide class of reinsurance policies and under the expected value reinsurance premium principle. These optimal reinsurance forms are more complicated than the optimal reinsurance contracts from the perspective of one party only. The proposed models can also be reduced to the problems of minimizing the VaR of one party's loss under the constraints on the interests of both the insurer and the reinsurer.