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跳扩散盈余过程的最优投资和最优再保险
引用本文:梁志彬.跳扩散盈余过程的最优投资和最优再保险[J].数学学报,2008,51(6):1195-120.
作者姓名:梁志彬
作者单位:南京师范大学数学与计算机学院
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.

关 键 词:随机控制  Hamilton-Jacobi-Bellman方程  跳扩散过程
收稿时间:2006-12-26
修稿时间:2008-6-4

Optimal Investment and Reinsurance for the Jump-Diffusion Surplus Processes
Institution:School of Mathematics and Computer Science, nanjing Normal University
Abstract: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.
Keywords:stochastic control  Hamilton-Jacobi-Bellman equation  jump-diffusion process
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