Uncertain fractional differential equations have been playing an important role in modelling complex dynamic systems. Early researchers have presented the extreme value theorems and time integral theorem on uncertain fractional differential equation. As applications of these theorems, this paper investigates the pricing problems of American option and Asian option under uncertain financial markets based on uncertain fractional differential equations. Then the analytical solutions and numerical solutions of these option prices are derived, respectively. Finally, some numerical experiments are performed to verify the effectiveness of our results.

中文翻译：

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基于不确定分数阶微分方程的期权定价公式

不确定的分数阶微分方程在复杂的动力系统建模中一直发挥着重要作用。早期的研究人员提出了不确定分数阶微分方程的极值定理和时间积分定理。作为这些定理的应用，本文基于不确定的分数阶微分方程，研究了不确定金融市场下美国期权和亚洲期权的定价问题。然后分别导出了这些期权价格的解析解和数值解。最后，进行了一些数值实验，以验证我们的结果的有效性。