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.