Optimal Liquidation Problems in a Randomly-Terminated Horizon

TL;DR

This paper investigates optimal asset liquidation strategies within a randomly-terminated timeframe, analyzing different scenarios under market impact models to understand how to minimize risk and costs amid horizon uncertainty.

Contribution

It introduces a framework for optimal liquidation in uncertain horizons, including verification of viscosity solutions and characterization of the value function for complex models.

Findings

Optimal strategies depend on horizon uncertainty and market impact parameters.

Viscosity solutions are verified for the associated HJB equations.

The value function is uniquely characterized as a viscosity solution.

Abstract

In this paper, we study optimal liquidation problems in a randomly-terminated horizon. We consider the liquidation of a large single-asset portfolio with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. Three different scenarios are analyzed under Almgren-Chriss's market impact model to explore the relation between optimal liquidation strategies and potential inventory risk arising from the uncertainty of the liquidation horizon. For cases where no closed-form solutions can be obtained, we verify comparison principles for viscosity solutions and characterize the value function as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation.