97 citations · 798 across the 62 of their papers we have counts for
39 papers · 1 filter
Itô's formula for flows of measures on semimartingales
Xin Guo, Huyên Pham, Xiaoli Wei
We establish Itô's formula along flows of probability measures associated with general semimartingales; this generalizes existing results for flows of measures on Itô processes. Ou…
Deep backward schemes for high-dimensional nonlinear PDEs
Côme Huré, Huyên Pham, Xavier Warin
We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equa…
Linear-Quadratic McKean-Vlasov Stochastic Differential Games
Enzo Miller, Huyen Pham
We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control…
Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis
Côme Huré, Huyên Pham, Achref Bachouch +1
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming app…
A Weak Martingale Approach to Linear-Quadratic McKean-Vlasov Stochastic Control Problems
Matteo Basei, Huyên Pham
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon pro\-blems, and all…
Zero-sum stochastic differential games of generalized McKean-Vlasov type *
Huyen Pham, Andrea Cosso
We study zero-sum stochastic differential games where the state dynamics of the two players is governed by a generalized McKean-Vlasov (or mean-field) stochastic differential equat…
Linear-quadratic McKean-Vlasov stochastic control problems with random coefficients on finite and infinite horizon, and applications
Matteo Basei, Huyên Pham
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon problems, and allow…
Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem
Elena Bandini, Andrea Cosso, Marco Fuhrman +1
We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in [4], we prove a corresponding randomized dynamic prog…
Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics
Erhan Bayraktar, Andrea Cosso, Huyên Pham
We analyze a stochastic optimal control problem, where the state process follows a McKean-Vlasov dynamics and the diffusion coefficient can be degenerate. We prove that its value f…
Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications *
Huyên Pham
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices i…
Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics
Huyên Pham, Xiaoli Wei
We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a lar…
Bellman equation and viscosity solutions for mean-field stochastic control problem
Huyên Pham, Xiaoli Wei
We consider the stochastic optimal control problem of McKean-Vlasov stochastic differential equation where the coefficients may depend upon the joint law of the state and control.…
Discrete time McKean-Vlasov control problem: a dynamic programming approach
Huyên Pham, Xiaoli Wei
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal d…
Randomization method and backward SDEs for optimal control of partially observed path-dependent stochastic systems
Elena Bandini, Andrea Cosso, Marco Fuhrman +1
We consider a unifying framework for stochastic control problem including the following features: partial observation, path-dependence (both with respect to the state and the contr…
BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data
Andrea Cosso, Huyên Pham, Hao Xing
We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convexity and superlinear nonlinearity in its gradient term, via a t…
Non-Markovian optimal stopping problems and constrained BSDEs with jump
Marco Fuhrman, Huyên Pham, Federica Zeni
We consider a non-Markovian optimal stopping problem on finite horizon. We prove that the value process can be represented by means of a backward stochastic differential equation (…
Ergodicity of robust switching control and nonlinear system of quasi variational inequalities
Erhan Bayraktar, Andrea Cosso, Huyên Pham
We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities. These equations are related to robust switching control pr…
Long time asymptotics for fully nonlinear Bellman equations: a Backward SDE approach
Andrea Cosso, Marco Fuhrman, Huyen Pham
We study the large time behavior of solutions to fully nonlinear parabolic equations of Hamilton-Jacobi-Bellman type arising typically in stochastic control theory with control bot…
Feynman-Kac representation of fully nonlinear PDEs and applications
Huyen Pham
The classical Feynman-Kac formula states the connection between linear parabolic partial differential equations (PDEs), like the heat equation, and expectation of stochastic proces…
Robust feedback switching control: dynamic programming and viscosity solutions
Erhan Bayraktar, Andrea Cosso, Huyen Pham
We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non st…
Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps
Idris Kharroubi, Nicolas Langrené, Huyên Pham
We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the F…
A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
Idris Kharroubi, Nicolas Langrené, Huyên Pham
We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representi…
Dual and backward SDE representation for optimal control of non-Markovian SDEs
Marco Fuhrman, Huyên Pham
We study optimal stochastic control problem for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients, and gain functionals are path-depend…
Reflected BSDEs with nonpositive jumps, and controller-and-stopper games
Sébastien Choukroun, Andrea Cosso, Huyen Pham
We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution is proved by a dou…