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考虑交易费用和债务的再保险和投资问题
  • ISSN号：1003-3998
  • 期刊名称：数学物理学报
  • 时间：2012.1
  • 页码：137-147
  • 分类：O224[理学—运筹学与控制论;理学—数学] F224.9[经济管理—国民经济]
  • 作者机构：[1]南京师范大学数学科学学院,南京210046
  • 相关基金：国家自然科学基金（10871098）、江苏省自然科学基金（BK2009397）和江苏省博士后科研基金（1001073C）资助
  • 相关项目：张量分解与最优化及其在信息处理中的应用
作者： 张昕丽|孙文瑜|
关键词： HJB方程, 债务, 比例再保险, 交易费用, Hamilton-Jacobi-Bellman equation, Liability, Proportional reinsurance, Transaction costs.
中文摘要：

该文考虑了保险公司的再保险和投资在多种风险资产中的策略问题．假设保险公司本身有着一定的债务，债务的多少服从线性扩散方程．保险公司可以通过再保险和将再保险之后的剩余资产投资在m种风险资产和一种无风险资产中降低其风险．资产中风险资产的价格波动服从几何布朗运动，其债务多少的演化也是依据布朗运动而上下波动．该文考虑了风险资产与债务之间的相互关系，考虑了在进行风险投资时的交易费用，并且利用HJB方程求得保险公司的最大最终资产的预期指数效用，给出了相应的最优价值函数和最优策略的数值解．

英文摘要：

In this paper, the authors consider a problem of optimal reinsurance and investment with multiple risky assets and a liability 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 while the liability evolves according to a Brownian motion with drift. The correlations between the risky assets and the liability are considered. The transaction costs produced during the investment are taken into account. Te authors consider the optimization problem of maximizing the expected exponential utility of terminal wealth 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.

同期刊论文项目
张量分解与最优化及其在信息处理中的应用
期刊论文 94 著作 1
解大型非线性规划，非线性半定规划和变分不等式的过滤集型方法的研究
期刊论文 41 会议论文 2
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期刊信息
  • 《数学物理学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院武汉物理与数学研究所
  • 主编：李邦河 陈贵强 朱熹平
  • 地址：湖北省武汉市武昌小洪山西路30号武汉71010信箱
  • 邮编：430071
  • 邮箱：actams@wipm.ac.cn
  • 电话：027-87199206
  • 国际标准刊号：ISSN：1003-3998
  • 国内统一刊号：ISSN：42-1226/O
  • 邮发代号:38-214
  • 获奖情况:
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  • 被引量:5382