Trading with Small Price Impact

51 Pages Posted: 28 May 2020

See all articles by Ludovic Moreau

Ludovic Moreau

Independent

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

H. Mete Soner

ETH Zürich - Department of Mathematics

Date Written: April 2017

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, viscosity solutions

Suggested Citation

Moreau, Ludovic and Muhle-Karbe, Johannes and Soner, H. Mete, Trading with Small Price Impact (April 2017). Mathematical Finance, Vol. 27, Issue 2, pp. 350-400, 2017, Available at SSRN: https://ssrn.com/abstract=3613151 or http://dx.doi.org/10.1111/mafi.12098

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

H. Mete Soner

ETH Zürich - Department of Mathematics ( email )

R¨amistrasse 101
Raemistr. 101
Z¨urich, 8092
Switzerland

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