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Qingxin Meng

Publications and source records attributed to Qingxin Meng.

44 records · Page 3Linked to original sources
arXiv2016

Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations with Jumps

In this paper, we study a linear-quadratic optimal control problem for mean-field stochastic differential equations driven by a Poisson random martingale measure and a multidimensional Brownian motion. Firstly, the existence and uniqueness of the optimal control is obtained by the classic convex variation principle. Secondly, by the duality method, the optimality system, also called the stochastic Hamilton system which turns out to be a linear fully coupled mean-field forward-backward stochastic differential equation with jumps, is derived to characterize the optimal control. Thirdly, applying a decoupling technique, we establish the connection between two Riccati equation and the stochastic Hamilton system and then prove the optimal control has a state feedback representation.

math.OC↗
arXiv2016

Forward and Backward Mean-Field Stochastic Partial Differential Equation and Optimal Control

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 first prove the continuous dependence theorems of forward and backward mean-field stochastic partial differential equations and show the existence and uniqueness of solutions to them. Then we establish necessary and sufficient optimality conditions of the control problem in the form of Pontryagin's maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study an example, an infinite-dimensional linear-quadratic control problem of mean-field type. Further an application to a Cauchy problem for a controlled stochastic linear PDE of mean-field type are studied.

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arXiv2012

Stochastic maximum principle for infinite dimensional control systems

The general maximum principle is proved for an infinite dimensional controlled stochastic evolution system. The control is allowed to take values in a nonconvex set and enter into both drift and diffusion terms. The operator-valued backward stochastic differential equation, which characterizes the second-order adjoint process, is understood via the concept of "generalized solution" proposed by Guatteri and Tessitore [SICON 44 (2006)].

math.OC↗
arXiv2010

Non-zero Sum Stochastic Differential Games of Fully Coupled Forward-Backward Stochastic Systems

In this paper, an open-loop two-person non-zero sum stochastic differential game is considered for forward-backward stochastic systems. More precisely, the controlled systems are described by a fully coupled nonlinear multi- dimensional forward-backward stochastic differential equation driven by a multi-dimensional Brownian motion. one sufficient (a verification theorem) and one necessary conditions for the existence of open-loop Nash equilibrium points for the corresponding two-person non-zero sum stochastic differential game are proved. The control domain need to be convex and the admissible controls for both players are allowed to appear in both the drift and diffusion of the state equations.

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arXiv2009

Optimal control problem of fully coupled forward-backward stochastic systems with Poisson jumps under partial information

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 differential equation driven by a Poisson random measure and an independent multi-dimensional Brownian motion, and all admissible control processes are required to be adapted to a given subfiltration of the filtration generated by the underlying Poisson random measure and Brownian motion. For this type of partial information stochastic optimal control problem, we give a necessary and sufficient maximum principle. All the coefficients appearing in the systems are allowed to depend on the control variables and the control domain is convex.

math.OC↗
arXiv2009

Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations

Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in the whole Euclidean space. Improved existence and uniqueness results are given in the Sobolev space $H^n$ ($=W^n_2$) under weaker assumptions than those used by X. Zhou [Journal of Functional Analysis 103, 275--293 (1992)]. As an application, a comparison theorem is obtained.

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