[1]张昕丽,孙文瑜.最小化损失概率的再保险和投资问题[J].南京师大学报(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.
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最小化损失概率的再保险和投资问题()
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《南京师大学报（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1; 2; 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 Xinli1; 2; Sun 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 equation; ruin probability; value function; transaction 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:

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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