In this review article, we present recent work on the regularity of dynamical market impact
models and their associated optimal order execution strategies. In particular, we address the …

In this paper we formulate the now classical problem of optimal liquidation (or optimal
trading) inside a mean field game (MFG). This is a noticeable change since usually …

The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …

This review article is intended to collect and summarize many of the results in the field of
optimal execution over the last twenty years. In doing so, we describe the general workings …

We develop a high frequency (HF) trading strategy where the HF trader uses her superior
speed to process information and to post limit sell and buy orders. By introducing a …

Through the analysis of a dataset of ultra high frequency order book updates, we introduce a
model which accommodates the empirical properties of the full order book together with the …

We prove a weak version of the dynamic programming principle for standard stochastic
control problems and mixed control-stopping problems, which avoids the technical …

This book exposes and comments on the consequences of Reg NMS and MiFID on market
microstructure. It covers changes in market design, electronic trading, and investor and …

This paper addresses portfolio liquidation using a new angle. Instead of focusing only on the
scheduling aspect like Almgren and Chriss in [J. Risk, 3 (2000), pp. 5--39], or only on the …

This paper deals with a stochastic order-driven market model with waiting costs, for
orderbooks with heterogenous traders. Offer and demand of liquidity drives price formation …