Optimal Investment Strategy with Ambiguity Aversion under the Exponential Premium Principle

Abstract

研究保险公司具有模糊厌恶情形下的最优投资问题。在近似扩散风险模型中，金融市场同时存在无风险投资和风险投资。考虑到金融市场具有复杂性的特点以及保险公司对自己的业务熟悉，假设金融市场模型存在模糊性而保险公司模型不存在模糊性，其中保险公司的保费收入通过指数保费原则计算。在最大化保险公司终端财富的期望效用值的目标下，根据动态规划原理方法给出了对应最优控制问题的Hamilton-Jacobi-Bellman (HJB)方程以及目标值函数，求出了值函数的解析解以及相应的最优投资策略的表达式。最后给出了数值算例阐述不同参数对最优投资策略值的影响。 The problem of optimal investment in the case of insurance companies with ambiguity aversion is studied. In the approximate diffusion risk model, there are risk-free investments and risky investments in the financial market. Considering the complexity of the financial market and the familiarity of the insurance company with its own business, it is assumed that there is ambiguity in the financial market model and no ambiguity in the insurance company model, where the premium income of the insurance company is calculated by the exponential premium principle. Under the objective of maximizing the expected utility value of the insurance company’s terminal wealth, the Hamilton-Jacobi-Bellman (HJB) equation and the objective value function corresponding to the optimal control problem are given according to the dynamic programming principle approach, and the analytical solutions of the value function and the expressions of the corresponding optimal investment strategies are derived. Finally, numerical examples are given to illustrate the effect of different parameters on the value of the optimal investment strategy.