A convex duality method for optimal liquidation with participation constraints

TL;DR

This paper introduces a flexible numerical method based on convex duality for approximating optimal trading strategies in large portfolio liquidation, accommodating complex costs and participation constraints.

Contribution

It presents a general convex duality-based numerical approach applicable to multi-asset portfolios with various execution costs and participation constraints, requiring minimal regularity assumptions.

Findings

Method effectively approximates optimal trading curves.

Applicable to multi-asset portfolios with complex costs.

Requires only $C^{1,1}$ regularity of Hamiltonian functions.

Abstract

In spite of the growing consideration for optimal execution in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to approximate the optimal strategy of a trader willing to unwind a large portfolio. The method we propose is very general as it can be applied to multi-asset portfolios with any form of execution costs, including a bid-ask spread component, even when participation constraints are imposed. Our method, based on convex duality, only requires Hamiltonian functions to have $C^{1,1}$ regularity while classical methods require additional regularity and cannot be applied to all cases found in practice.