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

Erhan Bayraktar, Thomas Cayé and Ibrahim Ekren

Mathematical Finance, 2021, vol. 31, issue 1, 36-108

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.

Date: 2021
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https://doi.org/10.1111/mafi.12283

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Working Paper: Asymptotics for Small Nonlinear Price Impact: a PDE Approach to the Multidimensional Case (2020)
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