ABSTRACT This paper aims to investigate optimal reinsurance contracts in a continuous-time modelling framework from the perspective of a principal-agent problem. The reinsurer plays the role of the principal and aims to determine an optimal reinsurance premium to maximize the expected utility on terminal wealth. It is supposed that the reinsurer faces ambiguity about the insurance claim process. The insurer acts as the agent whose objective is to determine an optimal retention level in a proportional reinsurance to maximize the expected utility on terminal wealth. It is postulated that the insurer is subject to a dynamic Value-at-Risk constraint, which may be attributed to capital requirements specified by Solvency II. The Hamilton-Jacobi-Bellman (HJB) dynamic programming is adopted to discuss the optimization problems of the reinsurer and insurer. Explicit expressions for the optimal solutions of the problems are obtained in the case of exponential utility functions. Numerical examples are provided to illustrate economic intuition and insights.

中文翻译：

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具有风险约束的稳健再保险合同

摘要本文旨在从委托代理问题的角度研究连续时间建模框架中的最佳再保险合同。再保险公司扮演委托人的角色，旨在确定最佳再保险保费，以最大化终端财富的预期效用。假设再保险公司在保险索赔过程中面临歧义。保险公司充当代理人，其目标是确定比例再保险中的最佳保留水平，以最大化终端财富的预期效用。假设保险公司受到动态风险价值约束，这可能归因于偿付能力 II 规定的资本要求。采用Hamilton-Jacobi-Bellman(HJB)动态规划来讨论再保险公司和保险公司的优化问题。在指数效用函数的情况下，获得了问题的最优解的显式表达式。提供了数字示例来说明经济直觉和见解。