Optimal dynamic excess-of-loss reinsurance and multidimensional portfolio selection  

作　　者：Bai LiHua Guo JunYi 

机构地区：[1]Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

出　　处：《Science China Mathematics》2010年第7期1784-1801,共18页中国科学：数学（英文版）

基　　金：supported by Keygrant Project of Ministry of Education, China (Grant No. 309009);National Natural Science Foundation of China (Grant No. 10871102)

摘　　要：In this paper, the surplus process of the insurance company is described by a Brownian motion with drift. In addition, the insurer is allowed to invest in a risk-free asset and n risky assets and purchase excess-of-loss reinsurance. Under short-selling prohibition, we consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the probability of ruin. We first show that the excess-of-loss reinsurance strategy is always better than the proportional reinsurance under two objective functions. Then, by solving the corresponding Hamilton-Jacobi-Bellman equations, the closed-form solutions of their optimal value functions and the corresponding optimal strategies are obtained. In particular, when there is no risky-free interest rate, the results indicate that the optimal strategies, under maximizing the expected exponential utility and minimizing the probability of ruin, are equivalent for some special parameter. This validates Ferguson's longstanding conjecture about the relation between the two problems.In this paper, the surplus process of the insurance company is described by a Brownian motion with drift. In addition, the insurer is allowed to invest in a risk-free asset and n risky assets and purchase excess-of-loss reinsurance. Under short-selling prohibition, we consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the probability of ruin. We first show that the excess-of-loss reinsurance strategy is always better than the proportional reinsurance under two objective functions. Then, by solving the corresponding Hamilton-Jacobi-Bellman equations, the closed-form solutions of their optimal value functions and the corresponding optimal strategies are obtained. In particular, when there is no risky-free interest rate, the results indicate that the optimal strategies, under maximizing the expected exponential utility and minimizing the probability of ruin, are equivalent for some special parameter. This validates Ferguson’s longstanding conjecture about the relation between the two problems.

关 键 词：EXPONENTIAL utility Hamilton-Jacobi-Bellman equation multiple risky ASSET investment proba- bility of RUIN excess-of-loss REINSURANCE 

分 类 号：N[自然科学总论]