马建静, 王过京. 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[J]. 应用概率统计, 2019, 35(2): 111-125. DOI: 10.3969/j.issn.1001-4268.2019.02.001
引用本文: 马建静, 王过京. 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[J]. 应用概率统计, 2019, 35(2): 111-125. DOI: 10.3969/j.issn.1001-4268.2019.02.001
MA Jianjing, WANG Guojing. An Optimal Reinsurance and Investment Problem with a Defaultable Security and a Stock with Ornstein-Uhlenbeck Process[J]. Chinese Journal of Applied Probability and Statistics, 2019, 35(2): 111-125. DOI: 10.3969/j.issn.1001-4268.2019.02.001
Citation: MA Jianjing, WANG Guojing. An Optimal Reinsurance and Investment Problem with a Defaultable Security and a Stock with Ornstein-Uhlenbeck Process[J]. Chinese Journal of Applied Probability and Statistics, 2019, 35(2): 111-125. DOI: 10.3969/j.issn.1001-4268.2019.02.001

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

An Optimal Reinsurance and Investment Problem with a Defaultable Security and a Stock with Ornstein-Uhlenbeck Process

  • 摘要: 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.

     

    Abstract: 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

     

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