Abstract

In this paper, we study the problem of excess-of-loss reinsurance and investment for an insurer who wishes to maximize the expected exponential utility of the terminal wealth. The surplus process of the insurer is described by a Brownian motion with drift, while the claim arrival process, the insurance and reinsurance premiums are affected by a stochastic factor. It is also assumed that the risky asset in the financial market have time varying and random coefficients. By applying the Hamilton-Jacobi-Bellman (HJB) equation approach, both the value function and the corresponding optimal strategies are obtained and characterized under different premium calculation principles. Furthermore, the existence and uniqueness of the solution to the HJB equation is also discussed. Finally, numerical examples are presented to illustrate our results.

摘要

在本文中，我们研究了希望最大化终端财富的预期指数效用的保险公司的超额损失再保险和投资问题。保险人的盈余过程用带有漂移的布朗运动来描述，而索赔到达过程、保险费和再保险费受随机因素的影响。还假设金融市场中的风险资产具有时变和随机系数。通过应用 Hamilton-Jacobi-Bellman (HJB) 方程方法，在不同的保费计算原则下，获得并表征了价值函数和相应的最优策略。此外，还讨论了HJB方程解的存在性和唯一性。最后，给出了数值例子来说明我们的结果。