Option Pricing for Uncertain Stock Model Based on Optimistic Value

Option pricing plays an important role in modern finance. This paper investigates the uncertain option pricing problems based on uncertainty theory by using the method to calculate the optimistic value of uncertain returns of options instead of the method of traditional expected value in the sense of the weighted average. The pricing formulas of the European and American options are derived for Liu’s uncertain stock model and Peng’s mean-reverting stock model which are two basic and representative uncertain stock models in uncertain finance. In the end, some numerical experiments are given to illustrate the effectiveness of the obtained results.