Optimal liquidation in a Level-I limit order book for large tick stocks

TL;DR

This paper develops a mathematical framework for optimal liquidation strategies in large-tick stocks' limit order books, modeling order events as Poisson processes and solving the problem via semi-Markov decision processes and dynamic programming.

Contribution

It introduces a novel semi-Markov decision process model for optimal liquidation in large-tick stocks, incorporating queueing theory and dynamic programming techniques.

Findings

Optimal liquidation policies are derived and numerically illustrated.

The framework effectively models order book dynamics with Poisson processes.

The approach maximizes expected terminal wealth within a fixed time horizon.

Abstract

We propose a framework to study the optimal liquidation strategy in a limit order book for large-tick stocks, with spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to independent Poisson processes, with parameters depending on price move directions. Our goal is to maximise the expected terminal wealth of an agent who needs to liquidate her positions within a fixed time horizon. Assuming that the agent trades (through sell limit order or/and sell market order) only when the price moves, we model her liquidation procedure as a semi-Markov decision process, and compute the semi-Markov kernel using Laplace method in the language of queueing theory. The optimal liquidation policy is then solved by dynamic programming, and illustrated numerically.