I think the problem with the reflecting barrier is located at equation (A.4).

Link to paper.

(A.4) dZt = (r-q)Yt dt + v Yt dWt + Yt dLt

where Yt is the price of the asset without the barrier, (r-q) are carry terms (q is dividend, r is interest rate), v is vol, dWt is diffusion term, and the process Lt is a ‘reflection function’. dZ is then the change in the asset price with barrier.

Thomas writes “The RGBM process as specified in equation (A.4)

*is a semimartingale*, because it can be decomposed into a local martingale (the Wiener term) and two finite variation processes, the drift and the reflection.”

But simulation shows that the process is negatively autocorrelated. Can a semimartingale be autocorrelated? Surely not.