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 …

Market makers continuously set bid and ask quotes for the stocks they have under
consideration. Hence they face a complex optimization problem in which their return, based …

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 …

We propose a minimal theory of non-linear price impact based on the fact that the (latent)
order book is locally linear, as suggested by reaction–diffusion models and general …

Limit Order Books (LOBs) serve as a mechanism for buyers and sellers to interact with each
other in the financial markets. Modelling and simulating LOBs is quite often necessary} for …

Evolutions of the trading landscape lead to the capability to exchange the same financial
instrument on different venues. Because of liquidity issues, the trading firms split large …

Classical models for order flow dynamics based on point processes, such as Poisson or
Hawkes processes, have been studied intensively. Often, several days of limit border book …

We propose two novel frameworks to study the price formation of an asset negotiated in an
order book. Specifically, we develop a game-theoretic model in many-person games and …