Optimal Asset Liquidation with Multiplicative Transient Price Impact

TL;DR

This paper develops explicit solutions for optimal asset liquidation in a market with multiplicative, transient, and non-linear price impacts, advancing understanding of optimal trading strategies under complex market effects.

Contribution

It introduces a novel multiplicative transient price impact model and derives explicit solutions for the associated singular optimal control problem.

Findings

Explicit solutions for optimal liquidation strategies.

Analysis of free boundary problems for different control constraints.

Enhanced modeling of transient price impacts in illiquid markets.

Abstract

We study a multiplicative transient price impact model for an illiquid financial market, where trading causes price impact which is multiplicative in relation to the current price, transient over time with finite rate of resilience, and non-linear in the order size. We construct explicit solutions for the optimal control and the value function of singular optimal control problems to maximize expected discounted proceeds from liquidating a given asset position. A free boundary problem, describing the optimal control, is solved for two variants of the problem where admissible controls are monotone or of bounded variation.