考虑交易费用和债务的再保险和投资问题

数学物理学报 ›› 2012, Vol. 32 ›› Issue (1): 137-147.

考虑交易费用和债务的再保险和投资问题

张昕丽, 孙文瑜

南京师范大学数学科学学院南京 210046

收稿日期:2010-06-15 修回日期:2011-07-04 出版日期:2012-02-25 发布日期:2012-02-25
基金资助:
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

Optimal Proportional Reinsurance and Investment with Transaction Costs and Liability

ZHANG Xin-Li, SUN Wen-Yu

School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046)

Received:2010-06-15 Revised:2011-07-04 Online:2012-02-25 Published:2012-02-25
Supported by:
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

摘要/Abstract

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.

关键词: HJB方程, 债务, 比例再保险, 交易费用

Abstract:

In this paper, the authorsconsidera problem ofoptimal reinsuranceand 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 investmentaretaken into account. Te authors considerthe optimization problemof 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.

Key words: Hamilton-Jacobi-Bellman equation, Liability, Proportional reinsurance, Transac-tion costs

中图分类号:

90B50

张昕丽, 孙文瑜. 考虑交易费用和债务的再保险和投资问题[J]. 数学物理学报, 2012, 32(1): 137-147.

ZHANG Xin-Li, SUN Wen-Yu. Optimal Proportional Reinsurance and Investment with Transaction Costs and Liability[J]. Acta mathematica scientia,Series A, 2012, 32(1): 137-147.

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