指数保费准则下基于Ornstein-Uhlenbeck过程的比例再保险与投资
Proportional Reinsurance and Investment Based on the Ornstein-Uhlenbeck Process under the Exponential Premium Principle
摘要: 本文研究了风险资产价格受Ornstein-Uhlenbeck过程影响下的最优投资与比例再保险问题。保险公司通过购买比例再保险，并将其财富投资于由无风险资产和风险资产构成的金融市场。采用扩散逼近模型刻画保险风险，并假设再保险保费按指数保费准则计算，同时考虑保险市场与金融市场之间存在相关性。保险公司的目标是最大化其终端财富的期望指数效用，应用随机控制理论和HJB方程，我们推导出了值函数与最优策略。最后，通过数值分析验证了模型参数对最优策略的影响。
Abstract: This paper investigates the optimal investment and proportional reinsurance problem when the price of the risky asset follows an Ornstein-Uhlenbeck process. The insurance company purchases proportional reinsurance and invests its wealth in a financial market consisting of a risk-free asset and a risky asset. The insurance risk is modeled using a diffusion approximation approach. The reinsurance premium is calculated under the exponential premium principle, and the correlation between the insurance market and the financial market is taken into account. The insurer aims to maximize the expected exponential utility of terminal wealth. By applying stochastic control theory and the Hamilton-Jacobi-Bellman (HJB) equation, we derive the value function and the optimal strategy. Finally, numerical analysis is conducted to illustrate the impact of model parameters on the optimal strategy.
文章引用：郭诗颖. 指数保费准则下基于Ornstein-Uhlenbeck过程的比例再保险与投资[J]. 应用数学进展, 2026, 15(6): 176-186. https://doi.org/10.12677/aam.2026.156275

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