181 citations · 548 across the 46 of their papers we have counts for
4 papers · 1 filter
The Self-Financing Equation in High Frequency Markets
Rene Carmona, Kevin Webster
High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal o…
Mean Field Games and Systemic Risk
Rene Carmona, Jean-Pierre Fouque, Li-Hsien Sun
We propose a simple model of inter-bank borrowing and lending where the evolution of the log-monetary reserves of banks is described by a system of diffusion processes coupled…
A probabilistic weak formulation of mean field games and applications
Rene Carmona, Daniel Lacker
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and contro…
Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics
René Carmona, Francois Delarue
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by t…