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An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps,…

Optimization and Control · Mathematics 2023-01-24 Taras Lukashiv , Yuliia Litvinchuk , Igor Malyk , Anna Golebiewska , Petr V. Nazarov

This paper is concerned with a linear quadratic (LQ, for short) optimal control problem for mean-field backward stochastic differential equations (MF-BSDE, for short) driven by a Poisson random martingale measure and a Brownian motion.…

Optimization and Control · Mathematics 2016-11-22 Maoning Tang , Qingxin Meng

The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it…

Probability · Mathematics 2022-12-09 Jun Gong , Huijie Qiao

We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…

Numerical Analysis · Mathematics 2025-02-10 Jiamin Jian , Qingshuo Song , Xiaojie Wang , Zhongqiang Zhang , Yuying Zhao

We consider the stochastic control of a semi-linear stochastic partial differential equations (SPDE) of McKean-Vlasov type. Based on a recent novel approach to the Lions derivative for Banach space valued functions, we prove the Gateaux…

Probability · Mathematics 2025-08-12 Johan Benedikt Spille , Wilhelm Stannat

We propose a decomposition method for solving a general class of linear-quadratic (LQ) McKean-Vlasov control problems involving conditional expectations and random coefficients, where the system dynamics are driven by two independent Wiener…

Optimization and Control · Mathematics 2026-04-15 Onésime Hounkpe , Dena Firoozi , Shuang Gao

In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…

Optimization and Control · Mathematics 2013-02-15 Nasir U. Ahmed , Charalambos D. Charalambous

A general stochastic maximum principle is proved for optimal controls of semilinear stochastic evolution equations. Stochastic evolution operators, and the control with values in a general set enter into both drift and diffusion terms.

Optimization and Control · Mathematics 2012-07-03 Kai Du , Qingxin Meng

In this paper, we study a class of stochastic optimal control problem with jumps under partial information. More precisely, the controlled systems are described by a fully coupled nonlinear multi- dimensional forward-backward stochastic…

Optimization and Control · Mathematics 2009-11-18 Qingxin Meng

We consider a symmetric $n$-player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players. Each player minimizes some expected cost by affecting the drift as well as the jump part of…

Probability · Mathematics 2018-05-14 Chiara Benazzoli , Luciano Campi , Luca Di Persio

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

Optimization and Control · Mathematics 2022-12-21 Justina Gianatti , Francisco J. Silva

We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…

Systems and Control · Electrical Eng. & Systems 2019-11-22 Zeji Yi , Zhefeng Cao , Evangelos Theodorou , Yongxin Chen

This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman's optimality principle and Pontryagin's maximum principle, and their modern exposition with…

Probability · Mathematics 2007-05-23 Huyen Pham

We analyze a stochastic optimal control problem, where the state process follows a McKean-Vlasov dynamics and the diffusion coefficient can be degenerate. We prove that its value function V admits a nonlinear Feynman-Kac representation in…

Probability · Mathematics 2016-11-15 Erhan Bayraktar , Andrea Cosso , Huyên Pham

A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…

Optimization and Control · Mathematics 2021-06-15 Giacomo Albi , Stefano Almi , Marco Morandotti , Francesco Solombrino

In this paper, we mainly focus on solving high-dimensional stochastic Hamiltonian systems with boundary condition, which is essentially a Forward Backward Stochastic Differential Equation (FBSDE in short), and propose a novel method from…

Optimization and Control · Mathematics 2021-12-13 Shaolin Ji , Shige Peng , Ying Peng , Xichuan Zhang

In this paper, we obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. The control is allowed to enter both diffusion and jump term and the control domain need not to…

Optimization and Control · Mathematics 2019-10-10 Yuanzhuo Song , Shanjian Tang , Zhen Wu

The objective of this paper is to weaken the Lipschitz condition to a monotonicity condition and to study the corresponding Pontryagin stochastic maximum principle (SMP) for a mean-field optimal control problem under monotonicity…

Optimization and Control · Mathematics 2025-03-18 Bowen He , Juan Li , Zhanxin Li

Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) with closed control regions are formulated and studied. Instead of using spike variation method as one may imagine, here we turn to…

Optimization and Control · Mathematics 2016-02-19 Tianxiao Wang , Haisen Zhang

This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of…

Optimization and Control · Mathematics 2017-11-01 Shaolin Ji , Xiaole Xue