A dynamic optimal execution strategy under stochastic price recovery

TL;DR

This paper develops a dynamic optimal execution strategy considering stochastic price recovery modeled by a Cox process, integrating market and limit orders, and solving a stochastic control problem to minimize market impact.

Contribution

It introduces a novel stochastic control framework for optimal execution that accounts for stochastic price recovery and combines market and limit orders.

Findings

The optimal strategy involves an initial large trade, small intermediate trades, and a final large trade.

Including limit orders improves execution performance under conservative price evaluation.

The strategy adapts dynamically based on market impact tolerance and state variables.

Abstract

In the present paper, we study the optimal execution problem under stochastic price recovery based on limit order book dynamics. We model price recovery after execution of a large order by accelerating the arrival of the refilling order, which is defined as a Cox process whose intensity increases by the degree of the market impact. We include not only the market order but also the limit order in our strategy in a restricted fashion. We formulate the problem as a combined stochastic control problem over a finite time horizon. The corresponding Hamilton-Jacobi-Bellman quasi-variational inequality is solved numerically. The optimal strategy obtained consists of three components: (i) the initial large trade; (ii) the unscheduled small trades during the period; (iii) the terminal large trade. The size and timing of the trade is governed by the tolerance for market impact depending on the state at each time step, and hence the strategy behaves dynamically. We also provide competitive results due to inclusion of the limit order, even though a limit order is allowed under conservative evaluation of the execution price.