跳扩散盈余过程的最优投资和最优再保险 |
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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. |
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作者姓名: | 梁志彬 |
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作者单位: | 南京师范大学数学与计算机学院 |
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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.
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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 |
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Institution: | School of Mathematics and
Computer Science, nanjing Normal University |
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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. |
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Keywords: | stochastic control Hamilton-Jacobi-Bellman equation jump-diffusion process |
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