Optimal solution of the liquidation problem under execution risk

TL;DR

This paper develops an extended mathematical model for optimal asset liquidation under execution risk, providing explicit solutions and advancing the understanding of trading strategies in stochastic environments.

Contribution

It extends the Almgren and Chriss model to incorporate execution risk and derives explicit solutions for the optimal liquidation strategy.

Findings

Explicit solutions for the extended model.

Enhanced understanding of liquidation under execution risk.

Mathematical framework for stochastic optimal control.

Abstract

We consider an investor that trades continuously and wants to liquidate an initial asset position within a prescribed time interval. During the execution of the liquidation order the investor is subject to execution risk. We study the problem of finding the optimal liquidation strategy adopted by the investor in order to maximize the expected revenue resulting from the liquidation. We present a mathematical model of the liquidation problem that extends the model of Almgren and Chriss (Almgren, R., Chriss, N., Optimal execution of portfolio transactions, Journal of Risk, 2000) to include execution risk. The liquidation problem is modeled as a linear quadratic stochastic optimal control problem with finite horizon and, under some hypotheses, is solved explicitly.