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Related papers: A duality approach to a price formation MFG model

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In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of…

Mathematical Finance · Quantitative Finance 2021-09-28 Masaaki Fujii , Akihiko Takahashi

Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.…

Analysis of PDEs · Mathematics 2017-10-05 David Evangelista , Rita Ferreira , Diogo A. Gomes , Levon Nurbekyan , Vardan Voskanyan

Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory,…

Machine Learning · Computer Science 2022-06-08 Lars Ruthotto , Stanley Osher , Wuchen Li , Levon Nurbekyan , Samy Wu Fung

Mean Field Game (MFG) systems describe equilibrium configurations in games with infinitely many interacting controllers. We are interested in the behavior of this system as the horizon becomes large, or as the discount factor tends to $0$.…

Optimization and Control · Mathematics 2019-03-13 Pierre Cardaliaguet , Alessio Porretta

In a probabilistic mean field game driven by a L\'evy process an individual player aims to minimize a long run discounted/ergodic cost by controlling the process through a pair of increasing and decreasing c\`adl\`ag processes, while he is…

Optimization and Control · Mathematics 2025-05-30 Facundo Oliú

In this paper, we focus on stationary (ergodic) mean-field games (MFGs). These games arise in the study of the long-time behavior of finite-horizon MFGs. Motivated by a prior scheme for Hamilton-Jacobi equations introduced in Aubry-Mather's…

Analysis of PDEs · Mathematics 2021-09-28 Tigran Bakaryan , Diogo Gomes , Héctor Sánchez Morgado

This paper deals with a stochastic order-driven market model with waiting costs, for order books with heterogenous traders. Offer and demand of liquidity drives price formation and traders anticipate future evolutions of the order book. The…

Trading and Market Microstructure · Quantitative Finance 2015-08-11 Aimé Lachapelle , Jean-Michel Lasry , Charles-Albert Lehalle , Pierre-Louis Lions

We employ the effective field theory approach for multi-field inflation which is a generalization of Weinberg's work. In this method the first correction terms in addition to standard terms in the Lagrangian have been considered. These…

High Energy Physics - Theory · Physics 2015-06-04 Nima Khosravi

In this paper, we are concerned with the inverse problem of determining anomalies in the state space associated with the stationary mean field game (MFG) system. We establish novel unique identifiability results for the intrinsic structure…

Analysis of PDEs · Mathematics 2025-05-14 Hongyu Liu , Catharine W. K. Lo

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…

Machine Learning · Computer Science 2023-01-05 Xin Guo , Anran Hu , Renyuan Xu , Junzi Zhang

We study Lagrangian systems on a closed manifold. We link the differentiability of Mather's beta-function with the topological complexity of the complement of the Aubry set. As a consequence, when the dimension of the manifold is less than…

Dynamical Systems · Mathematics 2007-05-23 Daniel Massart

This paper revisits well-studied dynamic decisions of weakly coupled large-population (LP) systems. Specifically, three types of LP decision problems: mean-field game (MG), mean-field team (MT), and mean-field-type control (MC), are…

Optimization and Control · Mathematics 2022-11-22 Huang Jianhui , Qiu Zhenghong , Wang Shujun , Wu Zhen

In this paper we study Mean Field Game systems under density constraints as optimality conditions of two optimization problems in duality. A weak solution of the system contains an extra term, an additional price imposed on the saturated…

Optimization and Control · Mathematics 2016-12-09 Pierre Cardaliaguet , Alpár Richárd Mészáros , Filippo Santambrogio

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear…

Analysis of PDEs · Mathematics 2017-04-25 Diogo Gomes , Levon Nurbekyan , Marc Sedjro

We review the recent approaches to modelling financial markets based on multi-agent systems. After a brief summary of the basic stylised facts observed in real-market time-series we discuss some simple agent-based systems which are…

Physics and Society · Physics 2008-12-02 Tobias Galla , Giancarlo Mosetti , Yi-Cheng Zhang

This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories…

Optimization and Control · Mathematics 2026-05-05 Pierre Lavigne , Quentin Petit , Xavier Warin

In this short note, we consider an inverse problem to a mean-field games system where we are interested in reconstructing the state-independent running cost function from observed value-function data. We provide an elementary proof of a…

Analysis of PDEs · Mathematics 2024-08-16 Kui Ren , Nathan Soedjak , Kewei Wang , Hongyu Zhai

We formulate and investigate a mean field optimization (MFO) problem over a set of probability distributions $\mu$ with a prescribed marginal $m$. The cost function depends on an aggregate term, which is the expectation of $\mu$ with…

Optimization and Control · Mathematics 2023-11-01 Kang Liu , Laurent Pfeiffer

A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton-Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption…

Analysis of PDEs · Mathematics 2016-11-29 Diogo A. Gomes , Levon Nurbekyan , Mariana Prazeres

Mean field games (MFG) and mean field control problems (MFC) are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative games with a…

Optimization and Control · Mathematics 2021-06-28 Andrea Angiuli , Jean-Pierre Fouque , Mathieu Lauriere