Yves Achdou Université ParisDiderot (France) Title: A Parcimonious Long Term Mean Field Model for Mining Industries (joint work with PN. Giraud, JM. Lasry and PL. Lions) 

Clémence Alasseur EDF R&D – FIME (France) Title: “An adverse selection approach to power tarification” (joint work with Ivar Ekeland, Romuald Elie, Nicola Hernández Santibáñez, Dylan Possomai) 

Imen Ben Tahar Université ParisDauphine (France) Title: Stylized model for a grid with distributed generation and storage 

Cédric Bernardin Université Nice Sophia Antipolis (France) Title: Diffusion versus superdiusion in a stochastic Hamiltonian lattice field model Abstract: In this talk I will review several recent works obtained in collaboration with M. Jara, P. Gonalves, M. Simon and M. Sasada about the energy diffusion in a Hamiltonian lattice field model with two conserved quantities perturbed by a conservative noise. I will discuss simple mechanisms that provide a crossover regime between the EdwardsWilkinson universality class, the ZeroPressure (3/4fractional superdifusion) universality class and the KPZ universality class. 

Mireille Bossy Inria (France) Title: PDE strategies for the existence of McKean Nonlinear diffusion models (joint work with Jean Francois Jabir, University of Valpareiso) 

Rainer Buckdahn Université de Bretagne Occidentale (France) Title: Meanfield SDE driven by a fractional Brownian motion and related stochastic control problem Abstract: We study a class of meanfield stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$ and a related stochastic control problem. We derive a Pontryagin type maximum principle and the associated adjoint meanfield backward stochastic differential equation driven by a classical Brownian motion, and we prove that under certain assumptions, which generalise the classical ones, the necessary condition for the optimality of an admissible control is also sufficient. The talk is baed on a joined work with Shuai Jing (Central University of Finance and Economy, Beijing, PRC) 

Ana Busic Inria (France) Title: Distributed demand control in power grids and ODEs for Markov decision processes (Joint work with Sean Meyn) 

Pierre Cardaliaguet Université ParisDauphine (France) Title: Long time behavior of Mean Field Games (joint work with A. Porretta) 

René Carmona Princeton University (USA) Title: Mean Field Games with Major and Minor Players: Theory and Numerics Abstract: We present a (possibly) new formulation of the mean field game problem in the presence of major and minor players, and give new existence results for linear quadratic models and models with finite state spaces. We shall also provide numerical results illustrating the theory and raising new challenges. 

JeanFrançois Chassagneux Université ParisDiderot (France) Title: Obliquely Reflected Backward Stochastic Differential Equations (joint work with A. Richou) 

Dan Crisan Imperial College London (UK) Title: Twodimensional pseudogravity model: particles motion in a nonpotential singular force field 

François Delarue Université Nice Sophia Antipolis (France) Title: Rough mean field differential equations 

Olivier Faugeras Inria (France) Title: Describing the thermodynamic limit of networks of interacting neurons 

JeanPierre Fouque University of California Santa Barbara (USA) Title: Systemic risk and stochastic games with delay Abstract: We propose a model of interbank lending and borrowing which takes into account clearing debt obligations. The evolution of logmonetary reserves of N banks is described by coupled diffusions driven by controls with delay in their drifts. Banks are minimizing their finitehorizon objective functions which take into account a quadratic cost for lending or borrowing and a linear incentive to borrow if the reserve is low or lend if the reserve is high relative to the average capitalization of the system. As such, our problem is a linearquadratic stochastic game with delay between N players. A unique openloop Nash equilibrium is obtained using a system of fully coupled forward and advanced backward stochastic differential equations. We then describe how the delay affects liquidity and systemic risk characterized by a large number of defaults. We also derive a closeloop Nash equilibrium using an HJB approach to this stochastic game with delay and we analyze its mean field limit. 

Benjamin Jourdain Ecole des Ponts, CERMICS (France) Title: Evolution of the Wasserstein distance between the marginals of two Markov processes (joint work with Aurélien Alfonsi and Jacopo Corbetta) Abstract: The Kantorovich duality leads to a natural candidate for the time derivative of the Wasserstein distance between the marginals of two Markov processes. Up to the sign, it is the sum of the integrals with respect to each of the two marginals of the corresponding infinitesimal generator applied to the corresponding Kantorovich potential. For pure jump processes with bounded intensity of jumps, we prove that the evolution of the Wasserstein distance is actually given by this candidate. 

Antoine Lejay Inria (France) Title: Estimation of the parameters of a discontinuous diffusion (Joint work with Paolo Pigato IECL / Inria Nancy GrandEst) Abstract: In this talk, we address the problem of the statistical estimation of the coefficients of a diffusion with piecewise constant coefficients (diffusivity and drift), called the oscillating Brownian motion. This problem of estimation shows a variety of behavior according to the respective signs of the drift, as the convergence is driven by the asymptotic behavior of the occupation time itself dependent of the regime of the diffusion (recurrent, null recurrent, transient). The oscillating Brownian motion could be seen as a continuous time version of the selfexciting threshold autoregressive (SETAR) model. Application to financial data shows estimations which are coherent with the one based on the SETAR model. It also empirically demonstrates the presence of leverage effect and/or meanreverting properties on some stock prices. 

Juan Li Shandong University (China) Title: Weak solutions of meanfield stochastic differential equations Abstract:In this talk we discuss weak solutions of meanfield stochastic differential equations (SDEs), also known as McKeanVlasov equations, whose drift $b(s, X_s,Q_{X_s})$, and diffusion coefficient $\sigma(s, X_s,Q_{X_s})$ depend not only on the state process $X_s$ but also on its law. We suppose that $b$ and $\sigma$ are bounded and continuous in the state as well as the probability law; the continuity with respect to the probability law is understood in the sense of the 2Wasserstein metric. Using the approach through a local martingale problem, we prove the existence and the uniqueness in law of the weak solution of meanfield SDEs. The uniqueness in law is obtained if the associated Cauchy problem possesses for all initial condition $f\in C_0^\infty({\mathbb R}^d)$ a classical solution. However, unlike the classical case, the Cauchy problem is a meanfield PDE as recently studied by Buckdahn, Li, Peng and Rainer (2014). In our approach, we also extend the It\^o formula associated with meanfield problems given by Buckdahn, Li, Peng and Rainer (2014) to a more general case of coefficients. 

PierreLouis Lions Collège de France (France) Title: Beyond stochastic control (and MFG) 

Sylvie Méléard Ecole Polytechnique (France) Title: Time scales and spectral gaps for quasi stationary distributions in large populations birth and death processes Abstract: We study a general class of birthanddeath processes that describe the size of populations going to extinction with probability one. The scale of the population is measured in terms of a ‘carrying capacity’ K. When K is large, the process is expected to stay close to its deterministic equilibrium during a long time but ultimately goes extinct. Our aim is to quantify the time for the process to reach the quasi stationary regime and the mean time to extinction in the quasi stationary distribution as a function of K, for large K. In dimension one, we also give a quantitative description of this quasistationary distribution. 

Sean Meyn University of Florida (USA) Title: Exponential Ergodicity in a Sobolev Space (coauthors: Adithya Devraj and Ioannis Kontoyiannis) 

Marcel Nutz Columbia University (USA) Title: Supply and Shorting in Speculative Markets 

Gilles Pagès Université Pierre et Marie Curie (France) Title: Nonasymptotic Gaussian Estimates for the Recursive Approximation of the Invariant Measure of a Diffusion Abstract: We obtain nonasymptotic Gaussian concentration bounds for the difference between the invariant measure of an ergodic Brownian diffusion process and the empirical distribution $\nu$ of an approximating scheme with decreasing time step along a suitable class of (smooth enough) test functions $f$ such that $f\nu(f)$ is a coboundary of the infinitesimal generator. We show that these bounds can still be improved when the (squared) Fr\”obenius norm of the diffusion coefficient lies in this class. We apply these bounds to design computable confidence intervals for the approximating scheme. As a theoretical application, we finally derive nonasymptotic deviation bounds for the almost sure Central Limit Theorem. 

Dylan Possamaï Université ParisDauphine (France) Title: Meanfield contract theory and electricity demand management 

Philip Protter Columbia University (USA) Title: Martingales and Strict Local Martingales Abstract: Whether a nonnegative solution of an SDE is a martingale or is a strict local martingale can, at times, have profound implications. Works of Delbaen, Shirakawa, Mijatovic, Urusov, Lions, Musiela, Andersen, Piterbarg, Bernard, Cui, and finally McLeish have studied the case of a one dimensional SDE, possibly with stochastic volatility. We will discuss two situations: (1) How a solution of an SDE which is a martingale can morph into a strict local martingale within a financial context by the addition of new information to the underlying filtration, and (2) how various components of a system of SDEs can be strict local martingales for some components of the system, and martingales for others. Our talk is based on joint work with Aditi Dandapani, Columbia PhD (2016), currently at ETHZurich. 

Wilhelm Stannat TU Berlin (Germany) Title: Stochastic Nerve Axon Equations 

Etienne Tanré Inria (France) Title: Network of interacting neurons Abstract:Some simple neuronal models evolve as follow: in the sub threshold regime, their membrane potential are solution of diffusion (each neuron is governed by independent noise). 

Stéphane Villeneuve Toulouse School of Economics (France) Title: PDE arising from principalagent problems 