Buy Low and Sell High

Abstract

In trading stocks investors naturally aspire to "buy low and sell high (BLSH)". This paper formalizes the notion of BLSH by formulating stock buying/selling in terms of four optimal stopping problems involving the global maximum and minimum of the stock prices over a given investment horizon. Assuming that the stock price process follows a geometric Brownian motion, all the four problems are solved and buying/selling strategies completely characterized via a free-boundary PDE approach.

Keywords: Black -- Scholes market, optimal stopping, stock goodness index, value function, free-boundary PDE (variational inequality)

JEL Classification: Q80, Q35, G60, G40, B91, B28