Abstract

In this paper, we explore the optimal insurance problem where the exclusion clause is taken into account. Assume that the insurable loss is mutually exclusive from another loss that is denied in the insurance coverage. Our objective is to characterize the optimal insurance strategy by minimizing the risk-adjusted value of a policyholder’s liability, where the unexpected loss is calculated by either the value at risk (VaR) or the tail value at risk (TVaR). To prevent moral hazard and to reflect the spirit of insurance, we analyze the optimal solutions over the class of ceded loss functions such that the policyholder’s retained loss and the proportion paid by an insurer are both increasing. We show that every admissible insurance contract is suboptimal to a ceded loss function composed of three interconnected line segments if the insurance premium principles satisfy risk loading and convex order preserving. The form of optimal insurance can be further simplified if the premium principles satisfies an additional weak property. Finally, we derive the optimal insurance explicitly for the expected value principle and Wang’s principle.

摘要

在本文中，我们探讨了考虑排除条款的最优保险问题。假设可保损失与保险范围内拒绝的另一损失相互排斥。我们的目标是通过最小化投保人负债的风险调整价值来表征最优保险策略，其中意外损失通过风险价值 ( VaR ) 或风险尾值 ( TVaR ) 计算）。为防止道德风险，体现保险精神，我们分析了投保人自留损失和保险人赔付比例均增加的分出损失函数类的最优解。我们表明，如果保险费原则满足风险加载和凸顺序保持，则每个可接受的保险合同对于由三个相互连接的线段组成的分出损失函数都是次优的。如果保费原则满足额外的弱属性，则最优保险的形式可以进一步简化。最后，我们明确地推导出了期望值原理和王氏原理的最优保险。