一类包含可违约资产和由Ornstein-Uhlenbeck过程刻画的股票的最优再保险和投资问题

摘要

In this paper,the insurer is allowed to buy reinsurance and allocate his money among three financial securities:a defaultable corporate zero-coupon bond,a default-free bank account,and a stock,while the instantaneous rate of the stock is described by an Ornstein-Uhlenbeck process.The objective is to maximize the exponential utility of the terminal wealth.We decompose the original optimization problem into two subproblems:a pre-default case and a post-default case.Using dynamic programming principle,and then solving the corresponding HJB equations,we derive the closed-form solutions for the optimal reinsurance and investment strategies and the corresponding value functions.%本文中,保险人被许可投资于三种金融资产:一个可违约公司零息债券,一个无违约风险的储蓄账户和一个股票.其中,股票的即时回报率由Ornstein-Uhlenbeck过程来刻画.保险人的目标是最大化终值财富的指数期望效用.我们将此优化问题分解为违约前和违约后两个问题,通过动态规划原理,然后求解对应的HJB方程,得到了最优策略和最优值函数的显式解.