延迟索赔风险模型的最优投资策略

详细信息    查看全文 | 推荐本文 |

英文篇名：OPTIMAL INVESTMENT STRATEGY FOR RISK MODEL OF DELAYED CLAIMS 作者：肖鸿民 ; 刘月娣 ; 刘爱玲 英文作者：XIAO Hong-min;LIU Yue-di;LIU Ai-ling;College of Mathematics and Statistics, Northwest Normal University; 关键词：延迟风险模型 ; 鞅中心极限定理 ; 最优投资 ; Hamilton-Jacobi-Bellman方程 英文关键词：delayed risk model;;martingale center limit theorem;;investment strategy;;Hamilton-Jacobi-Bellman equation 中文刊名：SXZZ 英文刊名：Journal of Mathematics 机构：西北师范大学数学与统计学院; 出版日期：2018-10-09 14:47 出版单位：数学杂志 年：2019 期：v.39;No.183 基金：国家自然科学基金项目(71261023) 语种：中文; 页：SXZZ201902014 页数：8 CN：02 ISSN：42-1163/O1 分类号：142-149

摘要

本文研究了延迟索赔风险模型最小化破产概率的最优投资决策问题.利用鞅中心极限定理将风险过程逼近为伊藤扩散过程,在此基础上将盈余投资于风险市场和无风险市场,采用随机马尔可大控制理论将其转化为相应的Hamilton-Jacobi-Bellman方程,获得了最优投资策略的显式表达式.得到的结果推广了延迟索赔风险模型的研究.
        In this paper, we study the optimal investment strategy of minimizing the ruin probability in the delayed risk model. By using martingale center limit theorem, the risk process is approximated to an Ito diffusion process. On the basis of this, the company invest its surplus into a risk market and a risk-free market. The stochastic Markov control theory is used to convert into the corresponding Hamilton-Jacobi-Bcllman equation, and explicit expression of optimal investment strategy is obtained. This result enriches the research of delayed claims risk model and has important reference value for risk management and control of insurance companies.

引文

[1] Embrechts P, Kl(u|¨)ppelberg C, Mikosch T. Modelling extremal events for insurance and finance[M].Berlin:Springer, 1997.
    [2] Asmussen S. Ruin probabilities[M]. Singapore:World Scientific, 2000.
    [3] Waters H R, Papatriandafylou A. Ruin probabilities allowing for delay in claims settlement[J]. Insurance Math. Econom., 1985, 4(2):113-122.
    [4] Yuen K C, Guo J Y. Ruin probabilities for time-correlated claims in the compound binomial model[J].Insurance Math. Econom., 2001, 29(1):47-57.
    [5] Yuen K C, Guo J Y, Ng K W. On ultimate ruin in a delayed-claims risk model[J]. J. Appl. Prob.,2005,42(1):163-174.
    [6]肖鸿民,王英,崔艳君.重尾分布L∩D下延迟索赔风险模型的精细大偏差[J].西北师范大学学报,2013,49(2):14-19.
    [7]肖鸿民,刘爱玲,何艳.相依赔付带投资的延迟风险模型的极限性质[J].兰州大学学报,2017, 53(5):696-700.
    [8] Schmidli H. Optimal proportional reinsurance policies in a dynamic setting[J]. Scand. Actuar. J.,2001, 2001(1):55-68.
    [9] Promislow D, Young V R. Minimizing the probability of ruin when claims follow brownian motion with drift[J]. N. Am. Actuar. J., 2005, 9(3):110-128.
    [10] Bi X C, Zhang S G. Minimizing the risk of absolute ruin under a diffusion approximation model with reinsurance and investment[J]. J. Sys. Sci. Comp., 2015, 28(1):144-155.
    [11] Bai L H, Cai J, Zhou M. Optimal meinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting[J].Insur. Math. Econom., 2013, 53(3):664-670.
    [12]张节松,肖庆宪.相依多险种模型的扩散逼近与最优投资[J].云南大学学报,2016, 38(3):362-368.
    [13] Liu C S, Yang H L. Optimal investment for an insurer to minimize its probability of ruin[J]. N. Am.Actuar. J., 2004, 8(2):11-31.
    [14]普兴成,张毅.随机微分方程及其在数理金融中的应用[M].北京:科学出版社,2010.