Optimal execution of Portfolio transactions with geometric price process

TL;DR

This paper derives the optimal trading strategy for executing large share transactions when prices follow a geometric Brownian motion, using accessible methods and considering temporary market impact.

Contribution

It introduces a new model for optimal execution with geometric price dynamics, contrasting with the traditional arithmetic models, and provides practical examples.

Findings

Optimal execution trajectory derived for geometric price process

Model incorporates general temporary impact function

Results illustrated with practical examples

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.