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

Satya N. Majumdar ¹, Jean-Philippe Bouchaud ²

Quantitative Finance 8 (2008) 753-760

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.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud
• 2. Science et Finance,
  Science et Finance