Stochastic Gradient Descent in the Optimal Control of Execution Costs

TL;DR

This paper introduces a stochastic gradient descent approach to approximate optimal execution cost policies in dynamic markets, addressing the challenge of deriving explicit solutions in complex market microstructures.

Contribution

It proposes a novel SGD-based methodology to derive near-optimal execution policies without requiring explicit mathematical solutions, adapting to evolving market conditions.

Findings

SGD can effectively refine execution strategies in complex markets.

The approach provides near-optimal policies with shorter computation times.

It bridges the gap between theoretical optimal policies and practical implementation.

Abstract

Bertsimas and Lo's seminal work laid the groundwork for addressing the implementation shortfall dilemma in institutional investing, emphasizing the significance of market microstructure and price dynamics in minimizing execution costs. However, the ability to derive a theoretical Optimum market order policy is an unrealistic assumption for many investors. This study aims to bridge this gap by proposing an approach that leverages stochastic gradient descent (SGD) to derive alternative solutions for optimizing execution cost policies in dynamic markets where explicit mathematical solutions may not yet exist. The proposed methodology assumes the existence of a mathematically derived optimal solution that is a function of the underlying market dynamics. By iteratively refining strategies using SGD, economists can adapt their approaches over time based on evolving execution strategies. While these SGD-based solutions may not achieve optimality, they offer valuable insights into optimizing policies under complex market frameworks. These results serve as a bridge for economists and mathematicians, facilitating the study of the Optimum policy volatile markets while offering SGD driven implementable policies that closely approximate optimal outcomes within shorter time frames.