This article and the companion paper aim at reviewing recent empirical and theoretical
developments usually grouped under the term Econophysics. Since the name was coined in …

… This model considers a market with N agents who can be part of two distinct groups of
traders: n f traders are ‘fundamentalists’, who share an exogenous idea p f of the value of the …

… where the forcing term f is the control. Our goal is to determine the existence and characterization
of those f that minimize the turbulence in f~. This particular choice of control is not of …

Motivated by the desire to bridge the gap between the microscopic description of price
formation (agent-based modeling) and the stochastic differential equations approach used …

… Several sections of this book were completed while Frederic Abergel was visiting the
Graduate School of Mathematical Sciences at the University of Tokyo, and the Laboratoire de …

This paper is devoted to the asymptotic behavior for some evolution equations when the
underlying Euclidean domain is unbounded. We present a method that is able to overcome the …

… book process is the operator L defined, for functions F : (a;b;μ) → F(a;b;μ) that are of class C
… In order to ease the already cumbersome notation, we have written F(ai;b;μ) instead of F(a1,.…

Lead/lag relationships are an important stylized fact at high frequency. Some assets follow
the path of others with a small time lag. We provide indicators to measure this phenomenon …

… ) is an early study of Hawkes processes applied to order book modelling, Hawkes-process-based
limit order book models are introduced and mathematically investigated in Abergel …

A limit order book provides information on available limit order prices and their volumes.
Based on these quantities, we give an empirical result on the relationship between the bid-ask …