Volume 31, Issue 1 p. 36-108
ORIGINAL ARTICLE

Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case

Erhan Bayraktar

Corresponding Author

Erhan Bayraktar

Department of Mathematics, University of Michigan, Ann Arbor, Michigan

Correspondence

Erhan Bayraktar, Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109.

Email: erhan@umich.edu

Search for more papers by this author
Thomas Cayé

Thomas Cayé

School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin, Ireland

Search for more papers by this author
Ibrahim Ekren

Ibrahim Ekren

Department of Mathematics, Florida State University, Tallahassee, Florida

Search for more papers by this author
First published: 20 July 2020
Citations: 2

Funding information:

Erhan Bayraktar was supported in part by the National Science Foundation (NSF) and the Susan M. Smith Professorship. Thomas Cayé was supported in part by the Swiss National Science Foundation (SNF) under grant 175133.

Abstract

We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small nonlinear price impact. In our model, cross-impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around its frictionless version. The leading order correction is characterized by a nonlinear second-order PDE related to an ergodic control problem and a linear parabolic PDE. We illustrate our result on a multivariate geometric Brownian motion price model.

DATA AVAILABILITY STATEMENT

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

The full text of this article hosted at iucr.org is unavailable due to technical difficulties.