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This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…

Optimization and Control · Mathematics 2017-02-17 Yi Zhuang

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…

Mathematical Finance · Quantitative Finance 2019-04-02 Philippe Casgrain , Sebastian Jaimungal

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex…

Optimization and Control · Mathematics 2017-10-10 Ying Hu , Jianhui Huang , Tianyang Nie

We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…

Probability · Mathematics 2018-08-24 Rene Carmona , Peiqi Wang

We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum…

Optimization and Control · Mathematics 2025-01-23 Alain Bensoussan , Ho Man Tai , Tak Kwong Wong , Sheung Chi Phillip Yam

This article is related to risk-sensitive nonzero-sum stochastic differential games in the Markovian framework. This game takes into account the attitudes of the players toward risk and the utility is of exponential form. We show the…

Optimization and Control · Mathematics 2014-12-04 Said Hamadène , Rui Mu

This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The…

Optimization and Control · Mathematics 2014-08-06 Said Hamadène , Rui Mu

This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by Carmona and Lacker, we consider a fully non-Markovian setting allowing for drift control and…

Probability · Mathematics 2023-12-25 Dylan Possamaï , Ludovic Tangpi

The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…

Probability · Mathematics 2014-08-13 Daniel Lacker

One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). Most existing methods are tailored to special cases in which the…

Optimization and Control · Mathematics 2023-09-20 Jiequn Han , Ruimeng Hu , Jihao Long

In this paper, we study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and global solutions are proved with some new ideas for a…

Probability · Mathematics 2024-02-02 Tao Hao , Ying Hu , Shanjian Tang , Jiaqiang Wen

In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose…

Probability · Mathematics 2017-07-31 Saran Ahuja , Weiluo Ren , Tzu-Wei Yang

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

Optimization and Control · Mathematics 2021-10-12 Xin Guo , Anran Hu , Renyuan Xu , Junzi Zhang

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 actions of the players in open-loop form. Finite and…

Probability · Mathematics 2018-12-04 Enzo Miller , Huyen Pham

We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish…

Optimization and Control · Mathematics 2022-05-06 Boualem Djehiche , Roxana Dumitrescu

We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE.…

Mathematical Finance · Quantitative Finance 2022-12-08 Guanxing Fu

In this paper we study the mean-field backward stochastic differential equations (mean-field bsde) of the form dY(t) =-f(t,Y(t),Z(t),K(t, . ),E[\varphi(Y(t),Z(t),K(t,.))])dt+Z(t)dB(t) +\int_{R_{0}}K(t,\zeta)\tilde{N}(dt,d\zeta), where B is…

Optimization and Control · Mathematics 2019-02-13 Nacira Agram , Yaozhong Hu , Bernt Øksendal

In this paper, we consider the mean field game with a common noise and allow the state coefficients to vary with the conditional distribution in a nonlinear way. We assume that the cost function satisfies a convexity and a weak monotonicity…

Optimization and Control · Mathematics 2021-05-26 Ziyu Huang , Shanjian Tang

This paper studies a nonlinear open-loop mean field Stackelberg stochastic differential game by using the probabilistic method through the FBSDE system and the idea of taking control as the fixed point. We successively construct the…

Optimization and Control · Mathematics 2026-01-08 Jianhui Huang , Qi Huang

We consider a class of extended mean field games with common noises, where there exists a strictly terminal constraint. We solve the problem by reducing it to an unconstrained control problem by adding a penalized term in the cost…

Optimization and Control · Mathematics 2025-06-10 Tianjiao Hua , Peng Luo