Xu, Feng; Zhou, Shengwu Pricing of perpetual American put option with sub-mixed fractional Brownian motion. (English) Zbl 1439.91035 Fract. Calc. Appl. Anal. 22, No. 4, 1145-1154 (2019). Summary: The pricing problem of perpetual American put options is investigated when the underlying asset price follows a sub-mixed fractional Brownian motion process. First of all, the sub-mixed fractional Black-Scholes partial differential equation is established by using the delta hedging method and the principle of no arbitrage. Then, by solving the free boundary problem, we get the pricing formula of the perpetual American put option. 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