Comment on “Time-changed geometric fractional Brownian motion and option pricing with transaction costs” by Hui Gu et al.

The purpose of this comment is to point out the inappropriate assumption of “3αH>1$3\alpha H>1$” and two problems in the proof of “Theorem 3.1” in section 3 of the paper “Time-changed geometric fractional Brownian motion and option pricing with transaction costs” by Hui Gu et al. [H. Gu, J.R. Liang, Y. X. Zhang, Time-changed geometric fractional Brownian motion and option pricing with transaction costs, Physica A 391 (2012) 3971–3977]. Then we show the two problems will be solved under our new assumption.