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山东大学学报(理学版) ›› 2015, Vol. 50 ›› Issue (05): 74-81.doi: 10.6040/j.issn.1671-9352.0.2014.316

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带投资和周期分红的布朗运动模型中的分红问题

王翠莲, 刘晓   

  1. 安徽师范大学数学计算机科学学院, 安徽 芜湖 241003
  • 收稿日期:2014-07-05 出版日期:2015-05-20 发布日期:2015-05-29
  • 通讯作者: 刘晓(1981-),男,博士,讲师,研究方向为随机控制与精算学.E-mail:yjjatyjjat@163.com E-mail:yjjatyjjat@163.com
  • 作者简介:王翠莲(1981-),女,硕士,讲师,研究方向为随机控制与精算学.E-mail:15905533625@163.com
  • 基金资助:
    国家自然科学基金资助项目(11201005);安徽省自然科学基金资助项目(1308085QA14);安徽省哲学社会科学规划资助项目(AHSK11-12D128)

On a periodic dividend problems in the Brownian motion model with investment

WANG Cui-lian, LIU Xiao   

  1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China
  • Received:2014-07-05 Online:2015-05-20 Published:2015-05-29

摘要: 假设分红只发生在一些随机的观测时间且按照障碍策略进行分红,得到了破产前折现分红随机变量的矩母函数、n阶矩函数和破产时间Laplace变换满足的微分方程,也得到了期望破产前折现分红和破产时间Laplace变换的显式表达式。

关键词: 分红, 投资, Laplace变换, 布朗运动

Abstract: Assume that the dividends can only be paid at some randomized observation times and dividends were paid according to a barrier strategy, the differential equations for the moment-generating function, the n-th moment function and the Laplace transform of ruin time were derived. The explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time were also obtained.

Key words: dividend, investment, Laplace transform, Brownian motion

中图分类号: 

  • O211.62
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