分数Black-Scholes市场中的动态下跌风险

数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1674-1682.

分数Black-Scholes市场中的动态下跌风险

张骅月¹|陈万华²|曲立安³

1.南开大学经济学院金融系 |天津300071|2.McMaster大学DeGroote商学院 L8S\ 4L8; 3.北京大学北京 100083

收稿日期:2008-04-10 修回日期:2011-07-12 出版日期:2011-12-25 发布日期:2011-12-25
基金资助:
国家自然科学基金(10901086)和国家重点基础研究发展计划(973计划) (2007CB814905)资助

Dynamic Below-Target Semi-Variance Risk Measure in a Fractional |Black-Scholes Market

ZHANG Hua-Yue¹, CHEN Wan-Hua², QU Li-An³

1.Department of Finance, School of Economics, Nankai University, Tianjin 300071;
2.DeGroote School of Business, |McMaster University, L8S 4L8;
3.Peking University, Beijing 100083

Received:2008-04-10 Revised:2011-07-12 Online:2011-12-25 Published:2011-12-25
Supported by:
国家自然科学基金(10901086)和国家重点基础研究发展计划(973计划) (2007CB814905)资助

摘要/Abstract

摘要：

该文讨论分数Black-Scholes市场上连续时间的资产组合模型. 首先, 找到基于BTSV的最小风险的可行资产组合；接着运用Cox和Huang提出的鞅方法^[1]得到最优期末财富及相应的最优投资策略. 最后, 借助数值分析法给出下跌风险的一些性质, 分析结果表明Hurst参数H是一个不可忽略的因素.

关键词: 下跌风险, 分数布朗运动, BTSV, Clark-Ocone定理

Abstract:

The paper is concerned with continuous time portfolio selection model in a complete Black-Scholes market driven by fractional Brownian motion with Hurst parameter H>1/2. The objective is to find an admissible portfolio π to minimize the risk measured by below target semi-variance. By the martingale method in Cox and Huang, we derive the optimal terminal wealth and the corresponding optimal investment strategy. Finally, we numerically analyze the properties of Downside risk measure, the result shows that Hurst index H must not be lost sight.

Key words: Downside risk, Fractional Brownian motion, BTSV, Clark-Ocone theorem, Lagrange multiplier

中图分类号:

60G15

张骅月, 陈万华, 曲立安. 分数Black-Scholes市场中的动态下跌风险[J]. 数学物理学报, 2011, 31(6): 1674-1682.

ZHANG Hua-Yue, CHEN Wan-Hua, QU Li-An. Dynamic Below-Target Semi-Variance Risk Measure in a Fractional |Black-Scholes Market[J]. Acta mathematica scientia,Series A, 2011, 31(6): 1674-1682.

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