基于Actor-Critic强化学习的再保险与投资问题
Reinsurance and Investment Problems Based on Actor-Critic Reinforcement Learning

本文研究了具有普通理赔和巨灾理赔两个业务线的保险公司的最优再保险和投资策略。它假设公司购买风险资产受到随机市场影响，索赔的时间和规模受到随机因素的影响，同时考虑金融市场和保险市场之间的共同冲击。建立了一个优化准则，以最大化在有限时间范围内保险公司的累积财富效用。然后，利用动态规划原理和It？公式，我们推导了Hamilton-Jacobi-Bellman (HJB)方程。由于扩散过程和状态切换的复杂性，很难找到精确的解，因此本文采用了数值方法(Actor-Critic强化学习算法)。最后，我们给出一个数值例子。
This paper studies the optimal reinsurance and investment strategies of insurance companies with two business lines: general claims and catastrophic claims. It assumes that the company’s purchase of risky assets is influenced by random market factors, and the timing and scale of claims are affected by random factors, while considering the joint impact between the financial market and the insurance market. An optimization criterion has been established to maximize the cumulative wealth utility of insurance companies within a limited time frame. Then, using the principles of dynamic programming and the It？ formula, we derived the Hamilton Jacobi Bellman (HJB) equation. Due to the complexity of the diffusion process and state switching, it is difficult to find an exact solution, so this paper adopts a numerical method (Actor-Critic reinforcement learning algorithm). Finally, we provide a numerical example.