Optimizing Execution Cost Using Stochastic Control

TL;DR

This paper presents an optimal stock execution strategy using discrete-time stochastic control, accounting for costs and risks, and compares it with existing methods based on historical data.

Contribution

It introduces a novel stochastic control-based approach for constrained stock execution that incorporates risk considerations and provides a mathematical framework for optimal allocation.

Findings

The proposed strategy effectively minimizes execution costs.

Incorporating risk into the model improves execution outcomes.

Compared with traditional methods, the new approach shows better performance on historical data.

Abstract

We devise an optimal allocation strategy for the execution of a predefined number of stocks in a given time frame using the technique of discrete-time Stochastic Control Theory for a defined market model. This market structure allows an instant execution of the market orders and has been analyzed based on the assumption of discretized geometric movement of the stock prices. We consider two different cost functions where the first function involves just the fiscal cost while the cost function of the second kind incorporates the risks of non-strategic constrained investments along with fiscal costs. Precisely, the strategic development of constrained execution of K stocks within a stipulated time frame of T units is established mathematically using a well-defined stochastic behaviour of stock prices and the same is compared with some of the commonly-used execution strategies using the historical stock price data.