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Related papers: A Variational Approach to Mean Field Type Control

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This paper is concerned with a class of linear-quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each…

Optimization and Control · Mathematics 2024-08-20 Min Li , Na Li , Zhen Wu

This paper is concerned with linear quadratic optimal control problems for mean-field backward stochastic differential equations (MF-BSDEs, for short) with deterministic coefficients. The optimality system, which is a linear mean-field…

Optimization and Control · Mathematics 2016-10-11 Xun Li , Jingrui Sun , Jie Xiong

We consider a problem of stochastic optimal control with separable drift uncertainty in strong formulation on a finite horizon. The drift coefficient of the state $Y^{u}$ is multiplicatively influenced by an unknown random variable…

Optimization and Control · Mathematics 2023-11-13 Samuel N. Cohen , Christoph Knochenhauer , Alexander Merkel

This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…

Computational Finance · Quantitative Finance 2014-06-26 Sakda Chaiworawitkul , Patrick S. Hagan , Andrew Lesniewski

We present a method for optimal control of systems governed by partial differential equations (PDEs) with uncertain parameter fields. We consider an objective function that involves the mean and variance of the control objective, leading to…

Optimization and Control · Mathematics 2017-11-27 Alen Alexanderian , Noemi Petra , Georg Stadler , Omar Ghattas

This paper studies a stochastic mean-field linear-quadratic Stackelberg differential game with random coefficients. The interaction between mean-field terms and random coefficients precludes the direct use of conventional decoupling…

Optimization and Control · Mathematics 2026-05-22 Ying Yang , Jie Xiong , Zhouyu Wang

We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the…

Optimization and Control · Mathematics 2017-02-07 Alain Bensoussan , Boualem Djehiche , Hamidou Tembine , Phillip Yam

This paper concerns a continuous time mean-variance (MV) portfolio selection problem in a jump-diffusion financial model with no-shorting trading constraint. The problem is reduced to two subproblems: solving a stochastic linear-quadratic…

Optimization and Control · Mathematics 2024-06-07 Xiaomin Shi , Zuo Quan Xu

Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild…

Optimization and Control · Mathematics 2014-02-13 Matanya B. Horowitz , Joel W. Burdick

We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…

Probability · Mathematics 2017-10-24 Ruoting Gong , Christian Houdré

We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using…

Probability · Mathematics 2013-09-25 Erhan Bayraktar , Mihai Sirbu

The objective of the present paper is to investigate the solution of fully coupled mean-field forward-backward stochastic differential equations (FBSDEs in short) and to study the stochastic control problems of mean-field type as well as…

Optimization and Control · Mathematics 2012-07-19 Ruimin Xu , Liangquan Zhang

In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli…

Optimization and Control · Mathematics 2023-01-24 Tianliang Zhang , Feiqi Deng , Peng Shi

In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…

Optimization and Control · Mathematics 2026-04-21 Jinniao Qiu

In this work, we study the optimal control of stochastic Burgers equation perturbed by Gaussian and Levy type noises with distributed control process acting on the state equation. We use the dynamic programming approach for the second order…

Analysis of PDEs · Mathematics 2022-04-18 Manil T. Mohan , K. Sakthivel , Sivaguru S. Sritharan

In this paper, we study the maximum principle of mean field type control problems when the volatility function depends on the state and its measure and also the control, by using our recently developed method. Our method is to embed the…

Optimization and Control · Mathematics 2023-09-14 Alain Bensoussan , Ziyu Huang , Sheung Chi Phillip Yam

Controlling systems of ordinary differential equations (ODEs) is ubiquitous in science and engineering. For finding an optimal feedback controller, the value function and associated fundamental equations such as the Bellman equation and the…

Optimization and Control · Mathematics 2021-04-14 Mathias Oster , Leon Sallandt , Reinhold Schneider

Stochastic optimal control problems governed by delay equations with delay in the control are usually more difficult to study than the the ones when the delay appears only in the state. This is particularly true when we look at the…

Probability · Mathematics 2021-03-22 F. Gozzi , F. Masiero

In this paper we study the stochastic control problem of partially observed (multi-dimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov…

Optimization and Control · Mathematics 2023-08-22 Yueyang Zheng , Yaozhong Hu

In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…

Probability · Mathematics 2020-09-15 Qian Lin