Drift dependence of optimal trade execution strategies under transient price impact

TL;DR

This paper provides a comprehensive solution for optimal trade execution strategies considering transient price impact and market drift, highlighting the importance of drift derivatives and the non-Markovian nature of the problem.

Contribution

It introduces a novel approach using singular stochastic control to solve a complex, non-Markovian trade execution problem with linear transient impact and drift dependence.

Findings

Optimal strategies depend on the derivative of the drift.

The problem is well-posed only if the drift is absolutely continuous.

Complete solutions are provided for minimizing liquidity costs and a cost-risk criterion.

Abstract

We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting.