Liu process is a basic process in fuzzy environment. As an extension of Liu process, fractional Liu process has attracted the attention of many scholars. In this paper, a fuzzy stock model driven by fractional Liu process is established, and its European, American, Asian, power options pricing formulas are given. In order to better understand these formulas, we give a few numerical examples to illustrate the changes of European option price with different parameters when time is fixed. However, these examples are not based on real-life data since the lack of parameter estimation method for fuzzy differential equation driven by Liu process. Then the changes of American option price are given when time and parameters are both changed. At the same time, we study the parameter interval where the option price fluctuates greatly. Finally, the fuzzy stock model is extended to the generalized case, and the stock price is given.

Liu过程是模糊环境中的一个基本过程。作为刘过程的延伸，分数刘过程引起了许多学者的关注。本文建立了由分数刘过程驱动的模糊股票模型，并给出了其欧、美、亚、权期权定价公式。为了更好地理解这些公式，我们举几个数值例子来说明时间固定时不同参数的欧式期权价格的变化。然而，由于缺乏刘过程驱动的模糊微分方程的参数估计方法，这些例子并不是基于现实生活中的数据。然后给出时间和参数都改变时美式期权价格的变化。同时，我们研究了期权价格波动较大的参数区间。最后，