Optimal trade execution in an order book model with stochastic liquidity parameters

TL;DR

This paper develops a model for optimal trade execution considering stochastic liquidity in a limit order book, deriving explicit solutions and analyzing strategic trading behaviors under randomness.

Contribution

It introduces a novel limit order book model with stochastic depth and resilience, providing explicit recursion formulas for minimal execution costs.

Findings

Explicit recursion for minimal costs derived

Optimal strategies analyzed for profitability and closing positions

Comparison with existing literature discussed

Abstract

We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both directions and at discrete points in time. We derive an explicit recursion that, under certain structural assumptions, characterizes minimal execution costs. We also discuss several qualitative aspects of optimal strategies, such as existence of profitable round trips or closing the position in one go, and compare our findings with the literature.