具有任意Hurst参数的分数次Black-Scholes模型的最优资产组合

数学物理学报

具有任意Hurst参数的分数次Black-Scholes模型的最优资产组合

刘韶跃; 杨向群

(湘潭大学数学与计算科学学院湖南 411105)

收稿日期:2006-01-17 修回日期:2007-12-12 出版日期:2008-08-25 发布日期:2008-08-25
通讯作者: 刘韶跃
基金资助:
湖南省教育厅青年项目(06B091)资助

Optimal Portfolio in a Fractional Black-Scholes Model with Arbitrary Hurst Parameter

Liu Shaoyue; Yang Xiangqun

(Department of Mathematics, Xiangtan University, Xiangtan 411105)

Received:2006-01-17 Revised:2007-12-12 Online:2008-08-25 Published:2008-08-25

摘要/Abstract

摘要： 在由具有任意Hurst参数H ∈(0,1)的分数次布朗运动驱动的Black-Scholes型市场数学模型的基础上, 运用拟条件数学期望和随机-梯度等工具,解决了其在能量型效应函数时的最优资产组合问题.

关键词: 分数次布朗运动, 分数次Black-Scholes模型, 最优资产组合

Abstract:

Based on the mathematical model for a Black-Scholes market driven by frctional Brownian motion B_H(t) with arbitrary Hurst parameter H ∈ (0,1), The authors solve the optimal portfolio problem in such a market for an agent with utility functions of power type by using quansi-conditional expectation and the stochastic-gradient.

Key words: Fractional Brownian motion, Black-Scholes model, Optimal porfolio

中图分类号:

90A12

刘韶跃; 杨向群. 具有任意Hurst参数的分数次Black-Scholes模型的最优资产组合[J]. 数学物理学报, 2008, 28(4): 742-746.

Liu Shaoyue; Yang Xiangqun. Optimal Portfolio in a Fractional Black-Scholes Model with Arbitrary Hurst Parameter[J]. Acta mathematica scientia,Series A, 2008, 28(4): 742-746.