Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies

TL;DR

This paper develops a unified framework for optimal portfolio liquidation considering small market impact and stochastic resilience, demonstrating convergence of strategies to semimartingale controls as impact diminishes.

Contribution

It introduces a novel convergence analysis for BSDEs with singular terminal conditions and unifies existing liquidation models using semimartingale strategies.

Findings

Convergence of optimal strategies to semimartingale controls as impact factor approaches zero.

New representation of BSDEs in terms of forward processes.

Framework encompasses the two main existing models in liquidation literature.

Abstract

We consider an optimal liquidation problem with instantaneous price impact and stochastic resilience for small instantaneous impact factors. Within our modelling framework, the optimal portfolio process converges to the solution of an optimal liquidation problem with general semimartingale controls when the instantaneous impact factor converges to zero. Our results provide a unified framework within which to embed the two most commonly used modelling frameworks in the liquidation literature and provide a microscopic foundation for the use of semimartingale liquidation strategies and the use of portfolio processes of unbounded variation. Our convergence results are based on novel convergence results for BSDEs with singular terminal conditions and novel representation results of BSDEs in terms of uniformly continuous functions of forward processes.