This paper investigates pricing formulas for geometric average and arithmetic average Asian call and put options under an uncertain exponential Ornstein–Uhlenbeck stock model. Employing the α-path technique from uncertainty theory, we derive closed-form integral representations for all four option types and rigorously establish their monotonicity properties with respect to the strike price, interest rate, time to expiration, and initial stock price. A comparative analysis with Liu’s standard uncertain stock model and a discussion of the option Greeks are also provided. Numerical examples are given to illustrate the practical applicability of the proposed formulas.
Yin et al. (Sat,) studied this question.