11 papers
Ergodic Linear-Quadratic Optimal Control with Stochastic Coefficients
Xuyang Lin, Nizar Touzi
We investigate ergodic linear-quadratic optimal control problems with stochastic coefficients and introduce the associated stochastic ergodic Hamilton-Jacobi-Bellman (HJB) equation…
Singular Backward SDEs for Optimal Control with State Constraints
Mathieu Lise, Nizar Touzi
We investigate a class of backward stochastic differential equations (BSDEs) with at most quadratic growth which explode at a possibly unbounded random horizon, defined through the…
Path-Dependent Ergodic Optimal Control and Backward Stochastic Differential Equations
Xuyang Lin, Mathieu Lise, Nizar Touzi
We investigate a new class of infinite-horizon backward stochastic differential equations for ergodic optimal control where the cost and state dynamics are time and path-dependent.…
Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian
Wenpin Tang, Nizar Touzi, Zikun Zhang +1
Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models pertur…
Bridging Schrödinger and Bass: A Semimartingale Optimal Transport Problem with Diffusion Control
Pierre Henry-Labordere, Grégoire Loeper, Othmane Mazhar +2
We study a semimartingale optimal transport problem interpolating between the Schrödinger bridge and the stretched Brownian motion associated with the Bass solution of the Skorokho…
Optimal resource allocation for maintaining system solvency
Gaoyue Guo, Wenpin Tang, Nizar Touzi
We study two optimal allocation problems for a system of independent Brownian agents whose states evolve under a limited shared control. At each time, a unit of resource can be div…
A PDE Derivation of the Schrödinger--Bass Bridge
Alexandre Alouadi, Pierre Henry-Labordère, Grégoire Loeper +3
This short paper announces the main results of \cite{SBB2026}, where the Schrödinger--Bass Bridge (SBB) problem is introduced and studied in full generality. Here we provide a dire…
LightSBB-M: Bridging Schrödinger and Bass for Generative Diffusion Modeling
Alexandre Alouadi, Pierre Henry-Labordère, Grégoire Loeper +3
The Schrodinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrodinger Bridge (SB). Building on th…
Sensitivity Analysis of Distributionally Robust BSDEs and RBSDEs
Arthur Compoint, Nathan Sauldubois, Nizar Touzi
We examine the sensitivity properties of backward stochastic differential equations and reflected backward stochastic differential equations, which naturally arise in the context o…
Branching diffusion representation for nonlinear Cauchyproblems and Monte Carlo approximation
Pierre Henry-Labordere, Nizar Touzi
We provide a probabilistic representations of the solution of some semilinear hyperbolicand high-order PDEs based on branching diffusions. These representations pave theway for a M…
A numerical algorithm for a class of BSDEs via branching process
Pierre Henry-Labordere, Xiaolu Tan, Nizar Touzi
We generalize the algorithm for semi-linear parabolic PDEs in Henry-Labordère (2012) to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching pro…