Exponential Ornstein–Uhlenbeck model for Asian barrier option pricing in uncertain environment

The valuation of options holds significant importance within financial markets, and among the various types of options, barrier options stand out. These options exhibit a unique characteristic where the option contract’s worthiness is contingent upon the underlying asset price reaching a predetermined level. The focus of this paper is to investigate the pricing of Asian barrier options in an uncertain environment. Specifically, it explores the pricing of these options when the underlying asset price follows the exponential Ornstein–Uhlenbeck Model. Additionally, the paper derives pricing formulas for four types of Asian barrier options (knock-in and knock-out) by utilizing \( \alpha \) $\alpha$ -paths of uncertain differential equations in this uncertain environment.