Optimal time to sell a stock in the Black–Scholes model: comment on ‘Thou shalt buy and hold’, by A. Shiryaev, Z. Xu and X.Y. Zhou

Abstract

We reconsider the problem of the optimal time to sell a stock studied by Shiryaev et al. (2008) (following in this issue of Quantitative Finance) using path integral methods. These methods allow us to confirm the results obtained by these authors and extend them to the entire parameter region. We also obtain the full distribution of the time tm at which the maximum of the price is reached for arbitrary values of the drift.