Optimal Investment Problem for an Insurer and a Reinsurer  

作　　者：LI Danping RONG Ximin ZHAO Hui 

机构地区：[1]School of Science, Tianjin University [2]Center for Applied Mathematics,Tianjin Uni-versity

出　　处：《Journal of Systems Science & Complexity》2015年第6期1326-1343,共18页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.11201335 and 11301376

摘　　要：This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. Moreover, the authors consider the correlation between the claim process and the price process of the risky asset. The authors first study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer. Then with the optimal reinsurance strategy chosen by the insurer, the authors consider two optimization problems for the reinsurer： The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability. By solving the corresponding Hamilton-Jacobi-Bellman equations, the authors derive the optimal reinsurance and investment strategies, explicitly. Finally, the authors illustrate the equality of the reinsurer＇s optimal investment strategies under the two cases.

关 键 词：Hamilton-Jacobi-Bellman equation optimal reinsurance and investment strategies proportional reinsurance ruin probability utility maximization 

分 类 号：F840.3[经济管理—保险] F224