Related papers: Stochastic Maximum Principle for Mean-field Contro…
The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not…
This paper study a type of fully coupled mean-field forward-backward stochastic differential equations with jumps under the monotonicity condition, including the existence and the uniqueness of the solution of our equation as well as the…
We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel…
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…
This paper is devoted to a global stochastic maximum principle for conditional mean-field forward-backward stochastic differential equations (FBSDEs, for short) with regime switching. The control domain is unnecessarily convex and the…
We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum…
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…
Hu et. al 2018 studied a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. By assuming a weakly coupled condition, they established an approach to obtain the…
This paper studies a nonlinear open-loop mean field Stackelberg stochastic differential game by using the probabilistic method through the FBSDE system and the idea of taking control as the fixed point. We successively construct the…
We study optimal control for mean-field forward backward stochastic differential equations with payoff functionals of mean-field type. Sufficient and necessary optimality conditions in terms of a stochastic maximum principle are derived. As…
We consider a class of extended mean field games with common noises, where there exists a strictly terminal constraint. We solve the problem by reducing it to an unconstrained control problem by adding a penalized term in the cost…
In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\Delta}Ss). Two types of FBS{\Delta}Ss are investigated. The first one is described by a partially…
In this paper, we consider a system of forward-backward stochastic differential equations (FBSDEs) with monotone functionals. We show the existence and uniqueness of such a system by the method of continuation similarly to Peng and Wu…
In this paper, we consider a partial observed two-person zero-sum stochastic differential game problem where the system is governed by a stochastic differential equation of mean-field type. Under standard assumptions on the coefficients,…
This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. We…
In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\Delta}Ss) where the uncertainty is modeled by a discrete time, finite state process, rather than…
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…
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…
In this paper, we first give the existence and uniqueness theorems for generalized mean-filed delay stochastic differential equations (GMFDSDEs) and mean-field anticipated backward stochastic differential equations (MFABSDEs). Then we study…
In this paper we present a numerical scheme to solve coupled mean field forward-backward stochastic differential equations driven by monotone vector fields. This is based on an adaptation of so called extragradient methods by characterizing…