Optimal execution of Portfolio transactions with geometric price process

Abstract

In this paper we derive the optimal execution trajectory for a trader who wishes to buy or sell a large position of shares which evolve as a geometric Brownian process in contrast to the arithmetic model which prevails in the existing literature, and with a general temporary impact $h$. We provide a couple of examples which illustrate the results. We would like to stress the fact that in this paper we use understandable user-friendly techniques.