Knock-in options are a type of barrier options which are path-dependent and get activated if the prices of underlying assets reach predetermined levels. This paper studies knock-in options in an uncertain market where the stock price follows a geometric process and the interest rate is dynamic. Pricing formulas of the knock-in call options and put options are derived by means of α-paths of uncertain differential equations. Numerical algorithms are designed and illustrated via some numerical experiments.

中文翻译：

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浮动利率的不确定股票模型的敲入期权

敲入期权是一类障碍期权，它们与路径有关，并且在基础资产的价格达到预定水平时会被激活。本文研究了在不确定的市场中，股票价格遵循几何过程且利率是动态的敲入期权。敲入看涨期权和看跌期权的定价公式是通过不确定微分方程的α路径得出的。通过一些数值实验设计并说明了数值算法。