Optimum Liquidation Problem Associated with the Poisson Cluster Process

TL;DR

This paper develops a discrete-time optimal liquidation strategy in illiquid markets, modeling order flow as a stochastic point process with price impact influenced by market microstructure, using PDMP-based Markov Decision Processes.

Contribution

It introduces a novel framework combining stochastic point processes and PDMPs for optimal liquidation in illiquid markets, accounting for market microstructure effects.

Findings

Optimal strategies depend on market microstructure characteristics.

Strategies involve placing offers at lower levels to avoid unfilled orders.

Numerical results validate the model's effectiveness.

Abstract

In this research, we develop a trading strategy for the discrete-time optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this framework, the flow of orders can be viewed as a point process with stochastic intensity. We model the price impact as a linear function of a self-exciting dynamic process. We formulate the liquidation problem as a discrete-time Markov Decision Processes, where the state process is a Piecewise Deterministic Markov Process (PDMP). The numerical results indicate that an optimal trading strategy is dependent on characteristics of the market microstructure. When no orders above certain value come the optimal solution takes offers in the lower levels of the limit order book in order to prevent not filling of orders and facing final inventory costs.