On the utility problem in a market where price impact is transient

TL;DR

This paper studies a discrete-time financial market model with transient price impact, demonstrating the existence of utility maximization solutions while relaxing previous market restrictions and addressing non-convexity in attainable portfolios.

Contribution

It introduces a more general model of transient price impact, removing restrictive assumptions and handling non-convex portfolio sets in utility maximization.

Findings

Existence of utility maximization solutions in the model

Relaxation of previous market restrictions

Handling of non-convex attainable portfolio sets

Abstract

We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage to remove some unnatural restrictions on the market depth and resilience processes that were present in earlier work. A non-standard feature of the problem is that the set of attainable portfolio values may fail the convexity property.