Optimal execution and price manipulations in time-varying limit order books

TL;DR

This paper extends the Limit Order Book model to include time-varying depth, solving the optimal execution problem and providing conditions to prevent price manipulations, offering insights into market maker behaviors.

Contribution

It introduces a generalized LOB model with dynamic depth and derives conditions to exclude price manipulations in both discrete and continuous settings.

Findings

Derived sufficient conditions to prevent price manipulations.

Provided solutions for optimal execution strategies in time-varying LOBs.

Gained qualitative insights into market maker behaviors regarding manipulations.

Abstract

This paper focuses on an extension of the Limit Order Book (LOB) model with general shape introduced by Alfonsi, Fruth and Schied. Here, the additional feature allows a time-varying LOB depth. We solve the optimal execution problem in this framework for both discrete and continuous time strategies. This gives in particular sufficient conditions to exclude Price Manipulations in the sense of Huberman and Stanzl or Transaction-Triggered Price Manipulations (see Alfonsi, Schied and Slynko). These conditions give interesting qualitative insights on how market makers may create or not price manipulations.