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>13αH>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.

► We point out the wrong assumption 3αH>13αH>1 and two problems in paper [1].
► The assumption is vital to the main Theorem of paper [1].
► The two problems will be solved under our new assumption.