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中文摘要：
考虑资产收益率分布的尖峰厚尾、长期相依和资产价格的均值回复性,选取具有尖峰厚尾和长期相依特征的Tsallis熵分布及均值回复性的O-U过程建立资产价格的运动模型,运用随机微分和等价测度鞅方法研究了幂型欧式期权的定价问题,得到了资产价格遵循最大化Tsallis熵分布的幂型欧式看涨及看跌期权的定价公式,该公式推广了经典的Black-Scholes公式,拓展了已有文献的结论。
英文摘要：
Characteristics of fat-tail,long-term dependence of return distribution and mean reversion of asset prices were considered. Thus,the distribution of Tsallis entropy,which has fat-tailed and long-term dependent characteristics,and O-U process were selected to describe the lawof the asset prices movement. By using the stochastic differential and martingale,the pricing of power European options was studied. The pricing formulas of power European call and put options,under the asset prices following the maximum Tsallis entropy distribution,were obtained,and the formulas not only generalize the classical Black-Scholes＇ conclusion,but also contain the conclusions in the other literatures.
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