Optimal Time to Sell a Stock in Black-Scholes Model: Comment on “Thou shall buy and hold”
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 tm at which the maximum of the price is reached for arbitrary values of the drift.