基于股票价格随机脉冲模型的保险人再保险和投资的最优动态组合选择

本文假设保险人可以进行再保险,并且允许其在金融市场中将资产投资于风险资产和无风险资产,其中风险资产价格采用随机脉冲模型来刻画.当目标是最大化在某一确定终止时刻所拥有财富的二次效用函数期望时,分别得到了超额损失再保险和比例再保险情况下保险人的再保险和投资最优动态选择的显式解和闭解.利用得到的显式解,考虑了金融风险和保险风险之间相关性对最优动态选择的影响,做了相关数值计算.

Optimal Dynamic Portfolio Section for Insurers with Investment and Reinsurance Based on Random Impulsive Model

In this paper an insurer is assumed to invest his reserve in a financial market, which consists of a risky asset and a risk-free asset. The random impulsive model for stock prices is used to depict the price of risky security. A controlled diffusion risk process is presented to describe such a dynamic setting. Explicit and closed-form solutions for the optimal dynamic choice are derived when excess-of-loss or proportional reinsurance is incorporated with an investment under the optimization criteria of maximizing the expectation of quadratic utility of the terminal wealth at a fixed terminal time, respectively. Based on the explicit solutions, the influence of the dependence between the finance risk and insurance risk on the optimal dynamic choice is illustrated numerically.