分数Black-Scholes市场中的动态下跌风险  

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

作　　者：张骅月[1] 陈万华 曲立安[3] 

机构地区：[1]南开大学经济学院金融系,天津300071 [2]McMaster大学DeGroote商学院,L8S4L8 [3]北京大学,北京100083

出　　处：《数学物理学报（A辑）》2011年第6期1674-1682,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(10901086);国家重点基础研究发展计划(973计划)(2007CB814905)资助

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.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.

关 键 词：下跌风险 分数布朗运动 BTSV Clark—Ocone定理 

分 类 号：O211.4[理学—概率论与数理统计]