具有投资利息的扰动复合Poisson风险模型的最优分红策略

数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1567-1578.

具有投资利息的扰动复合Poisson风险模型的最优分红策略

王春伟^1,2, 尹传存²

1.河南科技大学数学与统计学院 |河南洛阳 471003;
2.曲阜师范大学数学科学学院 |山东曲阜 273165

收稿日期:2009-10-13 修回日期:2011-09-07 出版日期:2011-12-25 发布日期:2011-12-25
基金资助:
国家自然科学基金(11171179)、高等学校博士点专项科研基金(20093705110002)、河南省基础与前沿技术研究项目(092300410178)和河南科技大学博士科研启动基金(09001443)资助

Optimal Dividend Strategy in |the Perturbed Compound Poisson Risk Model with Investment

WANG Chun-Wei^1,2, YIN Chuan-Cun²

1.School of Mathematics and Statistics, Henan University |of Science and Technology, Henan Luoyang |471003;
2.School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165

Received:2009-10-13 Revised:2011-09-07 Online:2011-12-25 Published:2011-12-25
Supported by:
国家自然科学基金(11171179)、高等学校博士点专项科研基金(20093705110002)、河南省基础与前沿技术研究项目(092300410178)和河南科技大学博士科研启动基金(09001443)资助

摘要/Abstract

摘要：

该文研究了具有投资利息的扰动复合Poisson风险模型的最优分红策略, 得到了一类使得最终折现分红总量达到最大值的分红策略. 作者刻画最优分红函数为与之相联系的HJB方程的粘性解, 并证明了一些特殊情形下最优分红策略的存在性.

关键词: Brown运动, 分红量, HJB方程, 投资利息, 最优分红策略

Abstract:

In this paper, we consider the optimal dividend strategy in the perturbed compound Poisson risk model with ivestment interest. Our aim is to find an optimal dividend strategy that maximizes the cumulative expected discounted dividend payments. We characterize the optimal value function as the viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation and prove that there exists an optimal barrier strategy which is optimal among all admissible dividend strategies in some special cases.

Key words: Brownian motion, Dividend payments, HJB equation, Investment interest, Optimal dividend strategy

中图分类号:

60J75

王春伟, 尹传存. 具有投资利息的扰动复合Poisson风险模型的最优分红策略[J]. 数学物理学报, 2011, 31(6): 1567-1578.

WANG Chun-Wei, YIN Chuan-Cun. Optimal Dividend Strategy in |the Perturbed Compound Poisson Risk Model with Investment[J]. Acta mathematica scientia,Series A, 2011, 31(6): 1567-1578.

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