基于MAP风险模型的最优分红问题研究

数学物理学报 ›› 2016, Vol. 36 ›› Issue (1): 176-186.

基于MAP风险模型的最优分红问题研究

陈旭, 杨向群

湖南师范大学数学与计算机学院, 高性能计算与随机信息处理省部共建教育部重点实验室长沙 410081

收稿日期:2015-07-06 修回日期:2015-12-13 出版日期:2016-02-25 发布日期:2016-02-25
作者简介:杨向群,xqyang@hunnu.edu.cn,14446811@qq.com
基金资助:
国家自然科学基金(11401204,11171101)资助

Optimal Dividend-Payout in a MAP Risk Model

Chen Xu, Yang Xiangqun

College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081

Received:2015-07-06 Revised:2015-12-13 Online:2016-02-25 Published:2016-02-25
Supported by:
Supported by the NSFC (11401204, 11171101)

摘要/Abstract

摘要：

在保险公司财务核算和分红均发生在随机时间点的假设条件下,讨论保险公司的最优分红问题.假设保险公司的盈余过程是经过MAP (马氏到达过程)的相过程调制的复合泊松过程,保险公司对盈余过程的观测和分红都发生在MAP的跳点上,以最大化期望折现分红总量为目标,证明了最优分红策略为band策略,并分析了经济状态和分红机会对值函数和分红策略的影响.

关键词: 折现分红总量, 随机观察, MAP, 贝尔曼方程

Abstract:

In this paper, we model the surplus process of the insurance by the classical compound Poisson risk model modulated by an continuous-time Markov chain, which is the phase process of a Markovian Arrival Process(MAP). The surplus process can't be observed continuously. The observation and the possible dividend are restricted to a sequence of random discrete time points which are determined by the same MAP. The insurance has only observation opportunities at some of these random time points, and has both observation and paying dividend opportunities at the other random time points. The object of the insurance is to select the dividend strategy that maximizes the expected total discounted dividend payments until ruin. The purpose of this paper is to analyze the impact of the paying dividend opportunity and the economic state on the value functions and dividend strategies. We show that the optimal dividend pay-out policy is a band policy at dividend pay-out times.

Key words: Discounted dividend payments, Randomized observation periods, MAP, Bellman equation

中图分类号:

O211.9

陈旭, 杨向群. 基于MAP风险模型的最优分红问题研究[J]. 数学物理学报, 2016, 36(1): 176-186.

Chen Xu, Yang Xiangqun. Optimal Dividend-Payout in a MAP Risk Model[J]. Acta mathematica scientia,Series A, 2016, 36(1): 176-186.

参考文献

[1] Finetti B De. Su un' impostazione alternativa della teoria collettiva del rischio. Transactions of the XVth Congress of Actuaries, 1957, 2:433-443
[2] Gao S, Liu Z M. The perturbed compound Poisson risk model with constant interest and a threshold strategy. Journal of Computational and Applied Mathematics, 2010, 233:2181-2188
[3] Lin S X, Pavlova K P. The compound Poisson risk model with a threshold dividend strategy. Insurance Math Econom, 2006, 38:57-80
[4] Chen X, Ou H. A compound Poisson model with proportional investment. Journal of Computational and Applied Mathematics, 2013, 242:248-260
[5] Loeffen R, Renaud J. De Fineti's optimal dividends problem with an affine penalty function at ruin. Insurance Math Econom, 2010, 46(1):98-108
[6] Albrecher H, Cheung E C K, Thonhauser S. Randomized observation periods for the compound Poisson risk model:the discounted penalty function. Scandinavian Actuarial Journal, 2013, 2013(6):424-452
[7] Albrecher H, Cheung E C K, Thonhauser S. Randomized observation periods for the compound Poisson risk model:Dividends. ASTIN Bulletion, 2011, 41(2):645-672
[8] Albrecher H, Bäuerle N, Thonhauser S. Optimal dividend-payout in random discrete time. Statistics and Risk Modeling, 2011, 28:251-276
[9] Cheung C K Eric, Landriault D. Perturbed MAP risk models with dividend barrier strategies. Journal of Applied Probability, 2009, 46(2):521-541
[10] Cheung C K Eric, Landriault D. A generallized penalty function with the maximum surplus prior to ruin in a MAP risk model. Insurance:Mathematics and Economics, 2010, 46(1):127-134
[11] Zhang Z, Yang H L, Yang H. On the absolute ruin in a MAP risk model with debit interest. Advances in Applied Probability, 2011, 43(1):77-96
[12] Mitric I R, Badescu A L, Stanford D A. On the absolute ruin problem in a Sparre Andersen risk model with constant interest. Insurance:Mathematics and Economics, 2012, 50:167-178
[13] Salah Z B, Morales M. Lévy systems and the time value of ruin for Markov additive processes. European Actuarial Journal, 2012, 2(2):289-317
[14] Bäuerler N, Rieder U. Markov Dicision Processes with Applications to Finance. New York:Springer, 2011