Optimal execution strategy in the presence of permanent price impact and fixed transaction cost

TL;DR

This paper models optimal trading strategies considering permanent price impact and fixed transaction costs, using impulse control and viscosity solutions, with numerical examples illustrating different impact scenarios.

Contribution

It introduces a comprehensive impulse control framework for optimal execution considering both permanent price impact and fixed costs, linking it with singular control when costs are absent.

Findings

Characterization of the value function via viscosity solutions.

Analysis of the no-transaction-cost case and its relation to singular control.

Numerical illustrations of impact effects on optimal strategies.

Abstract

We study a single risky financial asset model subject to price impact and transaction cost over an infinite horizon. An investor needs to execute a long position in the asset affecting the price of the asset and possibly incurring in fixed transaction cost. The objective is to maximize the discounted revenue obtained by this transaction. This problem is formulated first as an impulse control problem and we characterize the value function using the viscosity solutions framework. We also analyze the case where there is no transaction cost and how this formulation relates with a singular control problem. A viscosity solution characterization is provided in this case as well. We also establish a connection between both formulations with zero fixed transaction cost. Numerical examples with different types of price impact conclude the discussion.