Lévy过程驱动金融市场中最优资产组合复制策略

摘要

用白噪声分析的方法研究了Lévy过程驱动的金融市场.在Gauss白噪声和纯跳Lévy白噪声复合的Lévy白噪声框架下,给出了Clark-Haussmann-Ocone定理.应用此定理,分别在完全信息和部分信息下,用Malliavin导数表示了给定欧式期权的方差最小复制策略的具体形式,进一步用具体函数刻画了市场固有风险.分析结果表明,研究结果更贴近现实中一般的金融市场.%The financial market driven by Lévy processes is studied by white noise approach.The Clark-Haussmann-Ocone theorem is given under the framework of Lévy white noise,which is combined by Gaussian white noise and pure jump Lévy white noise.Applying the theorem,the minimal variance replicating portfolio for an European option is represented by Malliavin derivatives under full information and partial information.Furthermore,the explicit function is derived to describe the systematic risk.The analytical results show that the results are more appropriate for a general financial market in the real world.