Abstract

Option pricing plays an important role in modern finance. This paper investigates the uncertain option pricing problems based on uncertainty theory 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. The pricing formulas of the European and American options are derived by applying the method to calculate the optimistic value of uncertain returns of options instead of the usual method of expected value in the sense of the weighted average. In the end, some numerical experiments are given to illustrate the effectiveness of the obtained results.