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This paper is concerned with a linear-quadratic (LQ) Stackelberg mean field games of backward-forward stochastic systems, involving a backward leader and a substantial number of forward followers. The leader initiates by providing its…

Optimization and Control · Mathematics 2024-06-28 Wenyu Cong , Jingtao Shi

We propose a new method for the numerical solution of the forward-backward stochastic differential equations (FBSDE) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. Using Girsanov's…

Optimization and Control · Mathematics 2022-10-20 Kelsey P. Hawkins , Ali Pakniyat , Evangelos Theodorou , Panagiotis Tsiotras

In this paper, we propose a novel method to approximate the mean field stochastic differential equation by means of approximating the density function via Fokker-Planck equation. We construct a well-posed truncated Fokker-Planck equation…

Numerical Analysis · Mathematics 2025-03-25 Jinhui Zhou , Yongkui Zou , Shimin Chai , Boyu Wang , Ziyi Tan

We study the problem of optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in the case of \textit{partial…

Optimization and Control · Mathematics 2017-04-12 Roxana Dumitrescu , Bernt Øksendal , Agnès Sulem

This paper is devoted to the numerical resolution of McKean-Vlasov control problems via the class of mean-field neural networks introduced in our companion paper [25] in order to learn the solution on the Wasserstein space. We propose…

Optimization and Control · Mathematics 2024-03-20 Huyên Pham , Xavier Warin

This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…

Probability · Mathematics 2022-11-04 Yuanping Cui , Xiaoyue Li , Yi Liu , Chenggui Yuan

Mean-field stochastic differential equations, also called McKean--Vlasov equations, are the limiting equations of interacting particle systems with fully symmetric interaction potential. Such systems play an important role in a variety of…

Dynamical Systems · Mathematics 2025-09-15 Eirini Ioannou , Stefan Klus , Gonçalo dos Reis

In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward…

Probability · Mathematics 2007-11-21 Rainer Buckdahn , Juan Li , Shige Peng

In this paper we study a second-order mean-field stochastic differential systems describing the movement of a particle under the influence of a time-dependent force, a friction, a mean-field interaction and a space and time-dependent…

Probability · Mathematics 2022-10-10 T. C. Son , D. Q. Le , M. H. Duong

In this paper, we investigate a class of McKean-Vlasov stochastic differential equations under L\'evy-type perturbations. We first establish the existence and uniqueness theorem for solutions of the McKean-Vlasov stochastic differential…

Probability · Mathematics 2023-09-07 Ying Chao , Jinqiao Duan , Ting Gao , Pingyuan Wei

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost…

Optimization and Control · Mathematics 2012-10-11 Hamidou Tembine , Quanyan Zhu , Tamer Basar

This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the Wasserstein space. Because of the mean field structure of…

Probability · Mathematics 2017-03-07 Jean-François Chassagneux , Dan Crisan , François Delarue

An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.…

Optimization and Control · Mathematics 2016-02-26 Xun Li , Jingrui Sun , Jiongmin Yong

In this paper, our main aim is to investigate the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent $H\in(1/2, 1)$. After giving…

Numerical Analysis · Mathematics 2024-10-01 Shengrong Wang , Jie Xie , Li Tan

This paper studies a stochastic mean-field linear-quadratic optimal control problem with random coefficients. The state equation is a general linear stochastic differential equation with mean-field terms $\EE X(t)$ and $\EE u(t)$ of the…

Optimization and Control · Mathematics 2025-03-19 Yanyan Tang , Jie Xiong

In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters in both the driver…

Probability · Mathematics 2019-11-15 Boualem Djehiche , Romuald Elie , Said Hamadène

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for…

Probability · Mathematics 2015-01-06 Wen Lu , Yong Ren

We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the…

Probability · Mathematics 2020-03-03 Yinggu Chen , Boualem Djehiche , Said Hamadene

We consider the control of McKean-Vlasov dynamics (or mean-field control) with probabilistic state constraints. We rely on a level-set approach which provides a representation of the constrained problem in terms of an unconstrained one with…

Optimization and Control · Mathematics 2022-11-03 Maximilien Germain , Huyên Pham , Xavier Warin

This paper investigates first the existence and uniqueness of solutions for McKean-Vlasov forward-backward doubly stochastic differential equations (MV-FBDSDEs) in infinite-dimensional real separable Hilbert spaces. These equations combine…

Probability · Mathematics 2024-07-15 AbdulRahman Al-Hussein , Abdelhakim Ninouh , Boulakhras Gherbal