ABSTRACT We discuss an optimal excess-of-loss reinsurance contract in a continuous-time principal-agent framework where the surplus of the insurer (agent/he) is described by a classical Cramér-Lundberg (C-L) model. In addition to reinsurance, the insurer and the reinsurer (principal/she) are both allowed to invest their surpluses into a financial market containing one risk-free asset (e.g. a short-rate account) and one risky asset (e.g. a market index). In this paper, the insurer and the reinsurer are ambiguity averse and have specific modeling risk aversion preferences for the insurance claims (this relates to the jump term in the stochastic models) and the financial market's risk (this encompasses the models' diffusion term). The reinsurer designs a reinsurance contract that maximizes the exponential utility of her terminal wealth under a worst-case scenario which depends on the retention level of the insurer. By employing the dynamic programming approach, we derive the optimal robust reinsurance contract, and the value functions for the reinsurer and the insurer under this contract. In order to provide a more explicit reinsurance contract and to facilitate our quantitative analysis, we discuss the case when the claims follow an exponential distribution; it is then possible to show explicitly the impact of ambiguity aversion on the optimal reinsurance.

中文翻译：

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委托代理模型中具有模糊厌恶的最优超额损失再保险合同

摘要 我们讨论了在连续时间委托代理框架中的最优超额损失再保险合同，其中保险人（代理人/他）的盈余由经典的克拉姆-伦德伯格 (CL) 模型描述。除了再保险，保险公司和再保险公司（委托人/她）都可以将他们的盈余投资到包含一种无风险资产（例如短期利率账户）和一种风险资产（例如市场指数）的金融市场. 在本文中，保险公司和再保险公司是模糊规避的，并且对保险索赔（这与随机模型中的跳跃项有关）和金融市场的风险（这包括模型的扩散项）具有特定的建模风险规避偏好。再保险公司设计了一份再保险合同，在最坏的情况下最大化其最终财富的指数效用，这取决于保险公司的保留水平。通过采用动态规划方法，我们推导出最优稳健再保险合同，以及该合同下再保险人和保险人的价值函数。为了提供更明确的再保险合同并便于我们进行定量分析，我们讨论了索赔遵循指数分布的情况；这样就可以明确地表明歧义厌恶对最优再保险的影响。以及本合同项下再保险人和保险人的价值函数。为了提供更明确的再保险合同并便于我们进行定量分析，我们讨论了索赔遵循指数分布的情况；这样就可以明确地表明歧义厌恶对最优再保险的影响。以及本合同项下再保险人和保险人的价值函数。为了提供更明确的再保险合同并便于我们进行定量分析，我们讨论了索赔遵循指数分布的情况；这样就可以明确地表明歧义厌恶对最优再保险的影响。