arXiv research

Study on the smoothness of solutions to a specific type of stochastic differential equation.

Deep Galerkin Method estimates value function for mean-field control problem.

Let $X$be a complex hyperelliptic curve of genus two equipped with the canonical metric $ds^2$. We study mean field equations on complex hyperelliptic curves and show that the Gaussian curvature function of $(X,ds^2)$ determines an explicit solution to a mean field equation.

Existence of strong randomized equilibria in mean-field games with common noise.

New SDEs use $G$-Brownian motion, extending mean-field models.

Revises mean-field theory of Santa Fe model using kinetic theory.

We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition rate of $j$-th player is the sum of his control $α^j$ plus a minimum jumping rate $η$. Instead of working under monotonicity conditions, here we consider an anti-monotone running cost. We show that the mean …

Modeling pollution from competing firms using mean-field games.

Elman-type RNNs converge to globally optimal solutions in the mean-field regime.

The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.

Study on price formation among investors with exponential utility and liabilities.

New approach finds solutions to games with unbounded controls.

Conservative SPDEs emerge from fluctuating SGD dynamics in neural networks.

In this paper, we prove that the even solution of the mean field equation $Δu=λ(1-e^u)$ on $S^2$ must be axially symmetric when $4<λ\leq 8$. In particular, zero is the only even solution for $λ=6$. This implies the rigidity of Hawking mass for stable constant mean curvature(CMC) sphere with even symmetry.

We prove uniqueness of solutions to complex Monge-Ampère equations for small temperature.

Study explores optimal strategies in games with multiple players and mean-field interactions.

Mean field game with defaultable agents and systemic risk quantified.

Let $Ω$ be an annulus. We prove that the mean field equation $-Δψ=\frac{e\sp{-βψ}}{\int\sbΩe\sp{-βψ}} $ admits a solution with zero boundary for $β\in (-16π,-8π)$. This is a supercritical case for the Moser-Trudinger inequality.

Mean-field approximations simplify insurance liability calculations.

The paper proves existence of solutions for mean field equations on compact Riemann surfaces.

Study analyzes portfolio liquidation games influenced by self-exciting order flow.

We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence.

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from Pontryagin's stochastic maximum principle. Although the same cost functions as well…

Study on liquidation games with market drop-out, proving unique equilibria.

Develops asset pricing models with mean field game theory for heterogeneous agents.

A new method uses Mean Field Games to optimize mixture models of Bernoulli and categorical distributions.

Study policy gradient for large-agent mean-field control and game in continuous time.

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, industrial engineering, crowd motion, and more. In this paper, we provide a flexi…

Study shows how market firm capitalization models converge to stochastic PDE solutions.

In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the Banach-Picard iteration converges with geometrical convergence rate. When the be…

Study on market entry timing in stock liquidation with trading constraints.

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance function…

Model asset pricing with habit formation in a large market.

Study on kernel methods in large-scale machine learning problems.

Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an output function, and distinguishing metallic from insulating solutions. Both meta…

Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.

Study Nash equilibria in mean field portfolio games with consumption.

Paper analyzes SHB method for neural networks, proving stability, connectivity, and global convergence.

Study optimal investment strategies for competitive agents using Mean Field Games.

In this paper, we give an algebraic construction of the solution to the following mean field equation $Δψ+e^ψ=4π\sum_{i=1}^{2g+2}δ_{P_{i}},$ on a genus $g\geq 2$ hyperelliptic curve $(X,ds^{2})$ where $ds^{2}$ is a canonical metric on $X$ and $\{P_{1},\cdots,P_{2g+2}\}$ is the set of Weierstrass points on $X.$ Furt…

New algorithm controls large groups of devices to match energy demand signals.

Developed LQ MFG theory with common noise, proving existence and uniqueness.

Study of entropy-regularized LQG MFGs with exploratory actions.

Study time-inconsistent portfolio optimization for competitive agents with relative performance criteria.

Solves a game between brokers and informed traders using stochastic differential equations.

Given a regular bounded domain $Ω\subset\R{2m}$, we describe the limiting behavior of sequences of solutions to the mean field equation of order $2m$, $m\geq 1$, $(-Δ)^m u=ρ\frac{e^{2mu}}{\int_Ωe^{2mu}dx}\quad\text{in}Ω,$ under the Dirichlet boundary condition and the bound $0<ρ\leq C$. We emphasize the connection wi…

We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted spaces as well as a {convergence} result of the solution…

An informed broker optimizes trading strategies in a market influenced by many traders.