Related papers: Mean field social optimization: feedback person-by…
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…
This paper presents a novel model-free method to solve linear quadratic Gaussian mean field social control problems in the presence of multiplicative noise. The objective is to achieve a social optimum by solving two algebraic Riccati…
This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…
Mean field optimal control problems are a class of optimization problems that arise from optimal control when applied to the many body setting. In the noisy case one has a set of controllable stochastic processes and a cost function that is…
The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems…
In this manuscript, we investigate importance sampling methods for rare-event simulation in diffusion processes. We show, from a large-deviation perspective, that the resulting importance sampling estimator is log-efficient. This connection…
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…
In this paper, we present a scalable deep learning approach to solve opinion dynamics stochastic optimal control problems with mean field term coupling in the dynamics and cost function. Our approach relies on the probabilistic…
We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal…
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…
We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that…
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…
We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation we use the Hamilton--Jacobi--Bellman…
In a crowd model based on leader-follower interactions, where positions of the leaders are viewed as the control input, up-to-date solutions rely on knowledge of the agents' coordinates. In practice, it is more realistic to exploit…
This paper presents an application of mean field control to dynamic production optimization. Both noncooperative and cooperative solutions are considered. We first introduce a market of a large number of agents (firms) with sticky prices…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA…
The purpose of this work is to introduce a notion of weak solution to the master equation of a potential mean field game and to prove that existence and uniqueness hold under quite general assumptions. Remarkably, this is achieved without…