Stochastic impulse control on optimal execution with price impact and transaction cost

TL;DR

This paper models optimal asset trading considering price impact and transaction costs, formulating it as an impulse control problem and analyzing the value function via viscosity solutions and optimal stopping techniques.

Contribution

It introduces a novel impulse control framework for optimal execution with price impact and transaction costs, providing a characterization of the value function and bounds.

Findings

Value function characterized via viscosity solutions

Bounds established through associated optimal stopping problem

Framework applicable to realistic trading scenarios

Abstract

We study a single risky financial asset model subject to price impact and transaction cost over an finite time 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 as an impulse control problem and we characterize the value function using the viscosity solutions framework. We establish an associated optimal stopping problem that provides bounds and in some cases the solution of the value function.