Optimal Investment and Excess of Loss Reinsurance with Short-selling Constraint  

作　　者：Sheng Liu Jing-xiao Zhang 

机构地区：[1]Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, China

出　　处：《Acta Mathematicae Applicatae Sinica》2011年第3期527-534,共8页应用数学学报（英文版）

基　　金：Supported in part by the National Natural Science Foundation of China (No. 10771214);the Key research project of RUC, the Ministry of Education Humanities Social Science Key Research Institute in University Foundation (NO. 07JJD910244)

摘　　要：This paper considers the optimal control problem with constraints for an insurance company. The risk process is assumed to be a jump-diffusion process and the risk can be reduced through an excess of loss （XL） reinsurance. In addition, the surplus can be invested in the financial market. In the financial market, the short-selling constraint is one of the main factors which make models more realistic. Our goal is to find the optimal investment-reinsurance policy without short-selling, which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton-Jacobi-Bellman equation, the value function and the optimal investment-reinsurance policy are given in a closed form.This paper considers the optimal control problem with constraints for an insurance company. The risk process is assumed to be a jump-diffusion process and the risk can be reduced through an excess of loss （XL） reinsurance. In addition, the surplus can be invested in the financial market. In the financial market, the short-selling constraint is one of the main factors which make models more realistic. Our goal is to find the optimal investment-reinsurance policy without short-selling, which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton-Jacobi-Bellman equation, the value function and the optimal investment-reinsurance policy are given in a closed form.

关 键 词：Hamilton-Jacobi-Bellman equation jump-diffusion process short-selling constraint XL reinsurance 

分 类 号：O211.62[理学—概率论与数理统计] F842.3[理学—数学]