Asymptotics for Small Nonlinear Price Impact: A PDE Homogenization Approach to the Multidimensional Case

59 Pages Posted: 2 Jan 2019

See all articles by Erhan Bayraktar

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Thomas Cayé

Dublin City University - School of Mathematical Sciences

Ibrahim Ekren

Florida State University

Date Written: November 15, 2018

Abstract

Using ideas from homogenization theory and stability of viscosity solutions, we provide an asymptotic expansion of the value function of a multidimensional utility maximization problem with small non-linear 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. We illustrate our result on a multivariate geometric Brownian motion price model.

Keywords: utility maximization, portfolio choice, non-linear price impact, asymptotic expansion, viscosity solutions, homogenization

Suggested Citation

Bayraktar, Erhan and Cayé, Thomas and Ekren, Ibrahim, Asymptotics for Small Nonlinear Price Impact: A PDE Homogenization Approach to the Multidimensional Case (November 15, 2018). Available at SSRN: https://ssrn.com/abstract=3287099 or http://dx.doi.org/10.2139/ssrn.3287099

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Thomas Cayé

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

Ibrahim Ekren

Florida State University ( email )

1017 Academic Way,
224 LOVE Building
Tallahassee, FL 32306
United States
7342741176 (Phone)

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