具有PH(n)理赔时间间隔的Sparre-Andersen 模型中的分红问题

doi:10.6040/j.issn.1671-9352.0.2014.484

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (06): 7-12.doi: 10.6040/j.issn.1671-9352.0.2014.484

具有PH(n)理赔时间间隔的Sparre-Andersen 模型中的分红问题

刘晓

安徽师范大学数学计算机科学学院, 安徽芜湖 241003

收稿日期:2014-10-30 修回日期:2015-03-26 出版日期:2015-06-20 发布日期:2015-07-31
作者简介: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
基金资助:
安徽省哲学社会科学规划资助项目(AHSK11-12D128);安徽省教育厅自然科学研究重点项目(KJ2012ZD01);安徽省自然科学基金资助项目(1308085QA14);国家自然科学基金资助项目(11371321,11201005,11201006)

Dividend problems in a Sparre-Andersen model with PH(n) interclaim times

LIU Xiao

School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China

Received:2014-10-30 Revised:2015-03-26 Online:2015-06-20 Published:2015-07-31

摘要/Abstract

摘要： 假设盈余过程描述为Sparre-Andersen模型, 理赔时间间隔服从PH(n)分布, 分红只在一些随机的观测时间支付, 分红策略为障碍策略,得到了期望折现分红和破产时间Laplace变换所满足的积分-微分方程组,并在n=2和指数理赔的假设下给出了方程组的求解方法。

关键词: Sparre-Andersen模型, PH(n)分布, 分红, 随机观测

Abstract: Assuming that the surplus process is described by a Sparre-Andersen model, the interclaim times are PH(n) distributed, dividends can only be paid at some randomized observation times and the dividends are paid according to a barrier strategy, the integro-differential equations for the expected discounted dividends and the Laplace transform of ruin time were derived. The solutions of the equations were given with exponentially distributed claims and n=2.

Key words: Sparre-Andersen model, PH(n) distribution, dividend, randomized observation

中图分类号:

O211

刘晓. 具有PH(n)理赔时间间隔的Sparre-Andersen 模型中的分红问题[J]. 山东大学学报（理学版）, 2015, 50(06): 7-12.

LIU Xiao. Dividend problems in a Sparre-Andersen model with PH(n) interclaim times[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 7-12.

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具有PH(n)理赔时间间隔的Sparre-Andersen 模型中的分红问题

Dividend problems in a Sparre-Andersen model with PH(n) interclaim times

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