马尔科夫调节风险模型下的最优投资策略:最大化终端效用

本文用跳-扩散模型模拟保险公司的盈余过程,并允许该盈余在由1个无风险资产和N个风险资产组成的金融市场上进行投资.盈余过程和资产价格过程模型中的参数皆受到一个可观察的有限状态连续马尔科夫过程的影响.为了最大化终端效用,我们寻找最优的投资策略,借助HJB方程等工具问题得到解决.当公司的效用函数为指数型时,我们给出了最优投资策略与其对应的值函数的显示表达式,以及相关的经济解释.Browne (1995)和Yang和Zhang (2005)的一些结论得到推广.

Optimal Investment Strategy in a Markov-Modulated Risk Model: Maximizing the Terminal Utility

In this paper, the surplus of an insurance company is governed by a jump-diffusion process, and it can be invested in a financial market with one risk-free asset and $N$ risky assets. The parameters of surplus process and the asset price processes depend on the regime of the financial market, which is modeled by an observable finite-state continuous-time Markov chain. To maximize the terminal utility, we focus on finding optimal investment strategy and solve it by using the HJB equation. Explicit expression for optimal strategy and the corresponding objective function are presented when the company has an exponential utility function, some interesting economic interpretations are involved. Some known results of Browne (1995) and Yang and Zhang (2005) are extended.