An Optimal Reinsurance and Investment Problem with a Defaultable Security and a Stock with Ornstein-Uhlenbeck Process
MA Jianjing; WANG Guojing
Center for Financial Engineering, Soochow University, Suzhou, 215006, China; chool of Mathematics and Information Science, Shandong Technology and Business University, Yantai, 264005, China
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
The project was supported by the National Natural Science Foundation of China (Grant Nos. 11771320; 11871050) and the Shandong Natural Science Foundation (Grant No. ZR2013AM011).
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MA Jianjing; WANG Guojing. An Optimal Reinsurance and Investment Problem with a Defaultable Security and a Stock with Ornstein-Uhlenbeck Process. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2019, 35(2): 111-125.
