As applications of the uncertainty theory to finance, uncertain stock models have been presented to describe the prices of stocks strongly influenced by human uncertainty. So far, large progress has been achieved on pricing problems of path-independent options of the uncertain stock models. This paper investigates a type of path-dependent exotic options of an uncertain stock model which are named barrier options. Pricing formulas are derived based on the structure of the solutions of uncertain differential equations, and numerical algorithms are designed to calculate the prices of the barrier options based on these formulas.

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不确定股票模型的障碍期权定价公式

随着不确定性理论在金融领域的应用，人们提出了不确定性股票模型来描述受人为不确定性强烈影响的股票价格。到目前为止，在不确定的股票模型的与路径无关的期权的定价问题上已经取得了很大的进步。本文研究了一种不确定的股票模型中与路径相关的奇异期权，即障碍期权。基于不确定微分方程解的结构推导了定价公式，并设计了基于这些公式的数值算法来计算障碍期权的价格。