ABSTRACT

The Bowley solution refers to the optimal pricing density for the reinsurer and optimal ceded loss for the insurer when there is a monopolistic reinsurer. In a sequential game, the reinsurer first sets the pricing kernel, and thereafter the insurer selects the reinsurance contract given the pricing kernel. In this article, we study Bowley solutions under asymmetric information on the insurer's risk preferences where the identity of the insurer is unknown to the reinsurer. By assuming that the insurer adopts a Value-at-Risk measure or a convex distortion risk measure, the optimal pricing kernel for the insurer and the optimal ceded loss function for the reinsurer are determined. Numerical examples are presented to illustrate the results.

摘要

Bowley 解决方案是指当存在垄断再保险公司时，再保险公司的最优定价密度和保险公司的最优分出损失。在序列博弈中，再保险人首先设定定价核，然后保险公司选择给定定价核的再保险合同。在本文中，我们研究了保险公司风险偏好信息不对称下的 Bowley 解决方案，其中再保险公司不知道保险公司的身份。通过假设保险公司采用风险价值测度或凸扭曲风险测度，确定了保险公司的最优定价核和再保险公司的最优分出损失函数。给出了数值例子来说明结果。