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

Erhan Bayraktar, Thomas Caye and Ibrahim Ekren

Papers from arXiv.org

Abstract: We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption 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 and a linear parabolic PDE. We illustrate our result on a multivariate geometric Brownian motion price model.

Date: 2018-11, Revised 2020-06
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (2)

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Journal Article: Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case (2021)
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