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The paper is a full version of the short presentation in \cite{amv17}. Ergodic control for one-dimensional controlled diffusion is tackled; both drift and diffusion coefficients may depend on a strategy which is assumed markovian. Ergodic…

Probability · Mathematics 2020-09-01 Svetlana Anulova , Hilmar Mai , Alexander Veretennikov

In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two…

Optimization and Control · Mathematics 2018-10-30 Alain Bensoussan , Tao Huang , Mathieu Laurière

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…

Probability · Mathematics 2020-11-03 Masaaki Fujii

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…

Optimization and Control · Mathematics 2014-04-08 Boualem Djehiche , Hamidou Tembine , Raul Tempone

Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…

Optimization and Control · Mathematics 2022-10-03 Marc Abeille , Bruno Bouchard , Lorenzo Croissant

The purpose of this paper is to explore the necessary conditions for optimality of mean-field forward-backward delay control systems. A new estimate is proved, which is a powerfultool to deal with the optimal control problems of mean-field…

Optimization and Control · Mathematics 2018-11-06 Tao Hao , Qingxin Meng

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

We consider a Markov process on a Riemannian manifold, which solves a stochastic differential equation in the interior of the manifold and jumps according to a deterministic reset map when it reaches the boundary. We derive a partial…

Probability · Mathematics 2007-05-23 Julien Bect , Hana Baili , Gilles Fleury

In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths…

Probability · Mathematics 2017-02-21 Rainer Buckdahn , Juan Li , Jin Ma

This paper is concerned with a discounted optimal control problem of partially observed forward-backward stochastic systems with jumps on infinite horizon. The control domain is convex and a kind of infinite horizon observation equation is…

Optimization and Control · Mathematics 2022-01-04 Yueyang Zheng , Jingtao Shi

This work focuses on stability analysis of numerical solutions to jump diffusions and jump diffusions with Markovian switching. Due to the use of Poisson processes, using asymptotic expansions as in the usual approach of treating diffusion…

Optimization and Control · Mathematics 2014-07-11 Zhixin Yang , G. Yin , Haibo Li

While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward-forward problem is still poorly understood - even in the one-dimensional setting.…

Analysis of PDEs · Mathematics 2016-06-30 Diogo Gomes , Levon Nurbekyan , Marc Sedjro

For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…

Statistical Mechanics · Physics 2021-08-17 Cecile Monthus

We study Nash equilibria for a sequence of symmetric $N$-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative…

Probability · Mathematics 2022-01-19 Luciano Campi , Tiziano De Angelis , Maddalena Ghio , Giulia Livieri

Recent financial bubbles such as the emergence of cryptocurrencies and "meme stocks" have gained increasing attention from both retail and institutional investors. In this paper, we propose a game-theoretic model on optimal liquidation in…

Mathematical Finance · Quantitative Finance 2024-02-02 Ludovic Tangpi , Shichun Wang

We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable…

Machine Learning · Computer Science 2018-04-24 Jiachen Yang , Xiaojing Ye , Rakshit Trivedi , Huan Xu , Hongyuan Zha

We propose a method for obtaining maximum likelihood estimates (MLEs) of a Markov-Modulated Jump-Diffusion Model (MMJDM) when the data is a discrete time sample of the diffusion process, the jumps follow a Laplace distribution, and the…

Mathematical Finance · Quantitative Finance 2022-12-01 Laura Eslava , Fernando Baltazar-Larios , Bor Reynoso

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

In this paper we focus on the pathwise stability of mild solutions for a class of stochastic partial differential equations which are driven by switching-diffusion processes with jumps. In comparison to the existing literature, we show…

Probability · Mathematics 2015-03-13 Chenggui Yuan , Jianhai Bao

This paper studies indefinite stochastic linear-quadratic (LQ) optimal control for jump-diffusion systems with random coefficients. We construct an algebraic inverse flow from the zero-control base system, extract the semimartingale kernel…

Optimization and Control · Mathematics 2026-05-14 Xinyu Ma , Qingxin Meng