An Optimal Execution Problem in the Volume-Dependent Almgren-Chriss Model

TL;DR

This paper enhances the Almgren-Chriss optimal execution model by incorporating trading volume, proposing a penalization method for adaptive optimization, and analyzing the volume-weighted average-price strategy with asymptotic expansions.

Contribution

It introduces a volume-dependent process into the Almgren-Chriss model and develops a novel penalization approach for adaptive optimization.

Findings

Derived a verification theorem for the adaptive problem

Established the optimality of the VWAP strategy

Validated the asymptotic expansion numerically

Abstract

In this study, we introduce an explicit trading-volume process into the Almgren-Chriss model, which is a standard model for optimal execution. We propose a penalization method for deriving a verification theorem for an adaptive optimization problem. We also discuss the optimality of the volume-weighted average-price strategy of a risk-neutral trader. Moreover, we derive a second-order asymptotic expansion of the optimal strategy and verify its accuracy numerically.