Optimal Time to Sell a Stock in Black-Scholes Model: Comment on "Thou shall buy and hold", by A. Shiryaev, Z. Xu and X.Y. Zhou

英文摘要：

We reconsider the problem of optimal time to sell a stock studied recently by Shiryaev, Xu and Zhou using path integral methods. This method allows us to confirm the results obtained by these authors and extend them to a parameter region inaccessible to the method used by Shiryaev et. al. We also obtain the full distribution of the time t_m at which the maximum of the price is reached for arbitrary values of the drift.