跳扩散盈余过程的最优投资和最优再保险  

Optimal Investment and Reinsurance for the Jump-Diffusion Surplus Processes

作　　者：梁志彬[1] 

机构地区：[1]南京师范大学数学与计算机科学学院,南京210097

出　　处：《数学学报（中文版）》2008年第6期1195-1204,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10701082)

摘　　要：站在保险人的立场上,研究了跳扩散盈余过程的最优投资和最优再保险问题.在方差保费原理下,以盈余终值的期望指数效用达到最大作为最优准则,给出了最优策略和值函数的近似表达式.同时也证明了投资总比不投资好的结论.最后,通过一些数例和图表来进一步说明所获得的结论.We study, from the insurer＇s point of view, the optimal investment and proportional reinsurance for the jump-diffusion surplus processes. Assuming that the reinsurance premium is calculated according to the variance principle, we obtain the closed form expressions of the strategy and the value function which are optimal in the sense of maximizing the expected exponential utility from terminal wealth. We also conclude that the case with investment is always better than the one without investment. Some numerical examples are given, which illustrate the results of this paper.

关 键 词：随机控制 HAMILTON Jacobi—Bellman方程 跳扩散过程 

分 类 号：O211.63[理学—概率论与数理统计] O232[理学—数学]