To me this assumption may be the sticking point: "We assume that on the time scale of interest, the price is driftless, and write ..." unless you have constructed a pair (or basket) trade that is mean reverting, i.e., its returns obey driftless Brownian motion. But otherwise, it is a nice paper showing that a particular strategy using entry exit signals based on an ema signal (and mean reverting instrument) can be written exactly as a combination of hypergeometric distributions resembling the skewed log-normal returns of options... Of course, they never bothered to write down the solution which is the inverse Fourier transform of eqn (23). It's interesting that the solution only depends on the ratio Phi / (sigma * sqrt(tau)) -- where sigma*sqrt(tau) is the volatility over the memory length dictated by the Wiener process. In other words the shape of the profit distribution only depends on whether your +/- phi thresholds are larger or smaller than the expected volatility / memory of the process. Also it says nothing about cases where there is a real deviation from random walks which arguably is what people here are focused on.
Be careful second guessing Bouchaud and Potters. CFM hasn't done too badly. They're the Rentec of Europe.