Stock trading: an optimal selling rule (Q2719153)

The aim of this paper is to find a selling rule for stock trading. The stock behaviour is modelled using geometric Brownian motions and a finite state Markov chain. The author considers a set of target prices and stop-loss limits, their method then allows them to choose a target price and stop-loss limit in this set in order to maximise an expected reward function. The selling rule can be determined by solving a set of ODEs with two point boundary conditions. The author proves that the solution to these equations exists and is unique. In addition, the author derives the expected target period and the probability of making or losing money. A numerical example is condsidered.