Related papers: Forward utilities and Mean-field games under relat…
In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…
We propose a mean field game (MFG) framework to model the evolution of renewable energy production in competitive electricity markets. Producers interact through the spot price while optimising their profits under production, installation,…
This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…
We use the recently developed probabilistic analysis of mean field games with finitely many states in the weak formulation, to set-up a principal / agent contract theory model where the principal faces a large population of agents…
In this paper, using the mean-field game theory, we study a problem of equilibrium price formation among many investors with exponential utility in the presence of liabilities unspanned by the security prices. The investors are…
This paper studies multidimensional mean field games with common noise and the related system of McKean-Vlasov forward-backward stochastic differential equations deriving from the stochastic maximum principle. We first propose some…
We introduce a new class of forward performance processes that are endogenous and predictable with regards to an underlying market information set and, furthermore, are updated at discrete times. We analyze in detail a binomial model whose…
In this paper, we solve the time inconsistent portfolio selection problem by using different utility functions with a moving target as our constraint. We solve this problem by finding an equilibrium control under the given definition as our…
When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics…
We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value…
We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…
In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a…
This paper investigates a novel class of mean field games involving a major agent and numerous minor agents, where the agents' functionals are recursive with nonlinear backward stochastic differential equation (BSDE) representations. We…
In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations are the complex computations necessary to…
We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the…
We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time…
In this paper, we study two kinds of inverse problems for Mean Field Games (MFGs) with common noise. Our focus is on MFGs described by a coupled system of stochastic Hamilton-Jacobi-Bellman and Fokker-Planck equations. Firstly, we establish…
In this paper we provide an alternative framework to tackle the first-best Principal-Agent problem under CARA utilities. This framework leads to both a proof of existence and uniqueness of the solution to the Risk-Sharing problem under very…
An existence result for a class of mean field games of controls is provided. In the considered model, the cost functional to be minimized by each agent involves a price depending at a given time on the controls of all agents and a…
We consider an optimal investment-consumption problem for a utility-maximizing investor who has access to assets with different liquidity and whose consumption rate as well as terminal wealth are subject to lower-bound constraints. Assuming…