[1]张昕丽,孙文瑜.最小化损失概率的再保险和投资问题[J].南京师范大学学报(自然科学版),2013,36(01):1-9.
 Zhang Xinli,Sun Wenyu.Optimal Proportional Reinsurance and Investment with Minimizing Ruin Probability[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(01):1-9.
点击复制

最小化损失概率的再保险和投资问题()
分享到:

《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第36卷
期数:
2013年01期
页码:
1-9
栏目:
数学
出版日期:
2013-03-31

文章信息/Info

Title:
Optimal Proportional Reinsurance and Investment with Minimizing Ruin Probability
作者:
张昕丽12孙文瑜1
(1.南京师范大学数学科学学院,江苏 南京 210023) (2.聊城大学数学科学学院,山东 聊城 252000)
Author(s):
Zhang Xinli12Sun Wenyu1
(1.School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China) (2.School of Mathematical Sciences,Liaocheng University,Liaocheng 252000,China)
关键词:
HJB方程损失概率价值函数交易费用
Keywords:
Hamilton-Jacobi-Bellman equationruin probabilityvalue functiontransaction costs
分类号:
O224; F224.9
摘要:
本文考虑保险公司的再保险和投资策略问题.为了在降低风险的同时增加收益,保险公司会考虑在再保险的基础上将剩余财富投资到m种风险资产中.资产中风险资产的价格波动服从几何布朗运动.本文给出了考虑再保险和投资之后的财富模型,基于最小化损失概率的基础上求解其相应的HJB方程,从而给出保险公司的再保险和投资的最优策略.
Abstract:
In this paper,we consider a problem of optimal reinsurance and investment with multiple risky assets for an insurance company whose surplus is governed by a linear diffusion.The insurance company’s risk can be reduced through reinsurance,while,in addition,the company invests its surplus in a financial market with one risk-free asset and m risky assets.The risky assets’prices are governed by geometric Brownian motions.We consider the optimization problem of minimizing the ruin probability and solve it by using the corresponding Hamilton-Jacobi-Bellman(HJB)equation.Explicit expression for the optimal value function and the corresponding optimal strategies are obtained.

参考文献/References:

[1] Browne S.Survival and growth with liability:Optimal portfolio strategies in continuous time[J].Mathematics of Operations Research,1997,22(2):468-492.
[2]Emanuel D C,Harrison J M,Taylor A J.A diffusion approximation for the ruin probability with compounding assets[J].Scandinavian Actuarial Journal,1975(1):37-45.
[3]Hipp C,Plum M.Optimal investment for insurers[J].Insurance:Mathematics and Economics,2000,27(2):215-228.
[4]Schmidli H.Optimal proportional reinsurance policies in a dynamic setting[J].Scandinavian Actuarial Journal,2001(1):55-68.
[5]Schmidli H.On minimizing the ruin probability by investment and reinsurance[J].Annals of Applied Probability,2002,12(3):890-907.
[6]Taksar M,Markussen C.Optimal dynamic reinsurance policies for large insurance portfolios[J].Finance and Stochastics,2003,7(1):97-121.
[7]Browne S.Optimal investment policies for a firm with a random risk process:Exponential utility and minimizing the probability of ruin[J].Mathematics of Operations Research,1995,20(4):937-958.
[8]Yang H L,Zhang L H.Optimal investment for insurer with jump-diffusion risk process[J].Insurance:Mathematics and Economics,2005,37(3):615-634.
[9]Promislow D S,Young V R.Minimizing the probability of ruin when claims follow Brownian motion with drift[J].North American Actuarial Journal,2005,9(3):109-128.
[10]Luo S,Taksar M,Tsoi A.On reinsurance and investment for large insurance protfolios[J].Insurance:Mathematics and Economics,2008,42(1):434-444.
[11]Bai L H,Guo J Y.Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint[J].Insurance:Mathematics and Economics,2008,42(3):968-975.
[12]Sun W,Yuan Y.Optimization Theory and Methods:Nonlinear Programming[M].New York:Springer,2006.
[13]Fleming W H,Soner H M.Controlled Markov Processes and Viscosity Solutions[M].Berlin,New York:Springer,1993.
[14]Xu G L,Shreve S E.A duality methods for optimal consumption and investment under short-selling prohibition:Ⅱ constant market coefficients[J].Annals of Applied Probability,1992,2(2):314-328.

备注/Memo

备注/Memo:
收稿日期:2012-10-29.
基金项目:国家自然科学基金(11171159、11071122)、江苏省大规模复杂系统数值模拟重点实验室研究项目.
通讯联系人:张昕丽,博士后,讲师,研究方向:金融数学.E-mail:zhgylgp@gmail.com
更新日期/Last Update: 2013-03-31