Trading with Small Price Impact

48 Pages Posted: 1 Mar 2014 Last revised: 11 Apr 2017

See all articles by Ludovic Moreau

Ludovic Moreau

ETH Zurich - Department of Mathematics

Johannes Muhle-Karbe

Carnegie Mellon University - Department of Mathematical Sciences

Halil Mete Soner

ETH Zürich; Swiss Finance Institute

Date Written: March 30, 2015

Abstract

An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market, cost, and preference parameters. These results shed light on the general structure of the problem at hand, and also unveil close connections to optimal execution problems and to other market frictions such as proportional and fixed transaction costs.

Keywords: price impact, portfolio choice, asymptotics, homogenization

JEL Classification: G11, C61

Suggested Citation

Moreau, Ludovic and Muhle-Karbe, Johannes and Soner, Halil Mete, Trading with Small Price Impact (March 30, 2015). Swiss Finance Institute Research Paper No. 14-17. Available at SSRN: https://ssrn.com/abstract=2402245 or http://dx.doi.org/10.2139/ssrn.2402245

Ludovic Moreau

ETH Zurich - Department of Mathematics ( email )

R¨amistrasse 101
Z¨urich, 8092
Switzerland

Johannes Muhle-Karbe (Contact Author)

Carnegie Mellon University - Department of Mathematical Sciences ( email )

Pittsburgh, PA 15213-3890
United States

Halil Mete Soner

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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