Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion  

作　　者：Zhi-bin Liang 

机构地区：[1]Institute of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China [2]School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

出　　处：《Acta Mathematicae Applicatae Sinica》2007年第3期477-488,共12页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China(No.10571092)

摘　　要：In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.

关 键 词：Stochastic control Hamilton-Jacobi-Bellman equation JUMP-DIFFUSION brownian motion diffusion approximation proportional reinsurance 

分 类 号：O122[理学—数学]