arXiv subjects

Maoning Tang

Publications and source records attributed to Maoning Tang.

17 recordsLinked to original sources

arXiv2026

Viscosity Solutions of Hamilton--Jacobi--Bellman Equations for Control Systems Driven by Teugels Martingales

This paper studies discrete-time two-person nonzero-sum linear quadratic stochastic games with random coefficients. Using convex variational analysis, we derive necessary and sufficient conditions for the existence of open-loop Nash equilibria. When weighting matrices are indefinite, the classical first-order conditions are no longer sufficient for optimality; we introduce a global nonnegativity condition to restore sufficiency, which becomes a cornerstone of the subsequent analysis. To characterize the equilibria explicitly, we develop fully coupled forward-backward stochastic difference equations and a system of non-symmetric stochastic Riccati equations (FBS$\Delta$Es) with constraints. that decouple the stochastic Hamiltonian system. A key technical contribution is the provision of sufficient conditions -- positive semidefiniteness of the Riccati matrices operators and structural non-degeneracy -- that guarantee the invertibility of a related operator, ensuring the well-posedness of the closed-loop feedback representation of the open-loop Nash equilibrium strategies. A distinctive feature of this work is the presence of fully random coefficients, which leads to fully nonlinear higher-order backward stochastic difference equations in the Riccati framework, in contrast to the algebraic Riccati equations in the deterministic setting.

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arXiv2025

$H_2/H_\infty$ Control for Continuous-Time Mean-Field Stochastic Systems with Affine Terms

This paper discusses the $ H_2/H_{\infty} $ control problem for continuous-time mean-field linear stochastic systems with affine terms over a finite horizon. We employ the Mean-Field Stochastic Bounded Real Lemma (MF-SBRL), which provides the necessary and sufficient conditions to ensure that the $ H_{\infty} $ norm of system perturbations remains below a certain level. By utilizing the Mean-Field Forward-Backward Stochastic Differential Equations (MF-FBSDE), we establish the equivalence conditions for open-loop $ H_2/H_{\infty} $ control strategies. Furthermore, the paper demonstrates that the control problem is solvable under closed-loop conditions if solutions exist for four coupled Difference Riccati Equations (CDREs), two sets of backward stochastic differential equations (BSDEs) and ordinary equations (ODEs). The state-feedback gains for the control strategy can be derived from these solutions, thereby linking the feasibility of open-loop and closed-loop solutions.

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arXiv2024

Fully Coupled Nonlinear FBS$\Delta$Es: Solvability and LQ Control Insights

This paper explores a class of fully coupled nonlinear forward-backward stochastic difference equations (FBS$\Delta$Es). Building on insights from linear quadratic optimal control problems, we introduce a more relaxed framework of domination-monotonicity conditions specifically designed for discrete systems. Utilizing these conditions, we apply the method of continuation to demonstrate the unique solvability of the fully coupled FBS$\Delta$Es and derive a set of solution estimates. Moreover, our results have considerable implications for various related linear quadratic (LQ) problems, particularly where stochastic Hamiltonian systems are aligned with the FBS$\Delta$Es meeting these introduced domination-monotonicity conditions. As a result, solving the associated stochastic Hamiltonian systems allows us to derive explicit expressions for the unique optimal controls.

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arXiv2023

A Class of Forward-Backward Stochastic Differential Equations Driven by L\'{e}vy Processes and Application to LQ Problems

In this paper, our primary focus lies in the thorough investigation of a specific category of nonlinear fully coupled forward-backward stochastic differential equations involving time delays and advancements with the incorporation of L\'{e}vy processes, which we shall abbreviate as FBSDELDAs. Drawing inspiration from diverse examples of linear-quadratic (LQ) optimal control problems featuring delays and L\'{e}vy processes, we proceed to employ a set of domination-monotonicity conditions tailored to this class of FBSDELDAs. Through the application of the continuation method, we achieve the pivotal results of unique solvability and the derivation of a pair of estimates for the solutions of these FBSDELDAs. These findings, in turn, carry significant implications for a range of LQ problems. Specifically, they are relevant when stochastic Hamiltonian systems perfectly align with the FBSDELDAs that fulfill the domination-monotonicity conditions. Consequently, we are able to establish explicit expressions for the unique optimal controls by utilizing the solutions of the corresponding stochastic Hamiltonian systems.

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arXiv2017

Maximum Principle of Forward-Backward Stochastic Differential System of Mean-Field Type with Observation Noise

This paper is concerned with the partial information optimal control problem of mean-field type under partial observation, where the system is given by a controlled mean-field forward-backward stochastic differential equation with correlated noises between the system and the observation, moreover the observation coefficients may depend not only on the control process and but also on its probability distribution. Under standard assumptions on the coefficients, necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin's maximum principles are established in a unified way.

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arXiv2017

Partial Information Stochastic Differential Games for Backward Stochastic Systems Driven By L\'{e}vy Processes

In this paper, we consider a partial information two-person zero-sum stochastic differential game problem where the system is governed by a backward stochastic differential equation driven by Teugels martingales associated with a L\'{e}vy process and an independent Brownian motion. One sufficient (a verification theorem) and one necessary conditions for the existence of optimal controls are proved. To illustrate the general results, a linear quadratic stochastic differential game problem is discussed.

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arXiv2017

Partial Information Near-Optimal Control of Forward-Backward Stochastic Differential System with Observation Noise

This paper first makes an attempt to investigate the partial information near optimal control of systems governed by forward-backward stochastic differential equations with observation noise under the assumption of a convex control domain. By Ekeland's variational principle and some basic estimates for state processes and adjoint processes, we establish the necessary conditions for any $\varepsilon $-near optimal control in a local form with an error order of exact $\varepsilon ^{% \frac{1}{2}}.$ Moreover, under additional convexity conditions on Hamiltonian function, we prove that an $\varepsilon $-maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality.

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arXiv2017

A Revisit to Optimal Control of Forward-Backward Stochastic Differential System with Observation Noise

This paper revisits the partial information optimal control problem considered by Wang, Wu and Xiong [Wang et al 2013], where the system is derived by a controlled forward-backward stochastic differential equation with correlated noises between the system and the observation. For this type of partial information optimal control problem, one necessary and one suffcient (a verification theorem) conditions of optimality are derived using a unified way. We improve the $L^p-$ bounds on the control from $L^8$ in [Want et al 2013] to $L^4$ in this paper.

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arXiv2017

Optimal Control with State Constraints for Stochastic Evolution Equation with Jumps in Hilbert Space

This paper studies a stochastic optimal control problem with state constraint, where the state equation is described by a controlled stochastic evolution equation with jumps in Hilbert Space and the control domain is assumed to be convex. By means of Ekland variational principle, combining the convex variation method and the duality technique, necessary conditions for optimality are derived in the form of stochastic maximum principles.

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arXiv2017

Stochastic Evolution Equation Driven by Teugels Martingale and Its Optimal Control

The paper is concerned with a class of stochastic evolution equations in Hilbert space with random coefficients driven by Teugel's martingales and an independent multi-dimensional Brownian motion and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'evy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classic convex variation method and dual technique. The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

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arXiv2016

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

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. Firstly, by the classic convex variation principle, the existence and uniqueness of the optimal control is established. Secondly, the optimal control is characterized by the stochastic Hamilton system which turns out to be a linear fully coupled mean-field forward-backward stochastic differential equation with jumps by the duality method. Thirdly, in terms of a decoupling technique, the stochastic Hamilton system is decoupled by introducing two Riccati equations and a MF-BSDE with jumps. Then an explicit representation for the optimal control is obtained.

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arXiv2016

Maximum Principle for Partial Observed Zero-Sum Stochastic Differential Game of Mean-Field SDEs

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, the maximum principles for optimal open-loop control in a strong sense as well as a weak one are established by the associated optimal control theory in Tang and Meng (2016). To illustrate the general results, a class of linear quadratic stochastic differential game problem is discussed and the existence and dual characterization for the partially observed open-loop saddle are obtained.

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arXiv2016

Stochastic Evolution Equations of Jump Type with Random Coefficients: Existence, Uniqueness and Optimal Control

We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classic convex variation method and dual technique. The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation with jumps which our theoretical results can solve.

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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.

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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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arXiv2011

Optimal Variational Principle for Backward Stochastic Control Systems Associated with Lévy Processes

The paper is concerned with optimal control of backward stochastic differential equation (BSDE) driven by Teugel's martingales and an independent multi-dimensional Brownian motion, where Teugel's martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see Nualart and Schoutens \cite{NuSc}). We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria (called backward linear-quadratic problem, or BLQ problem for short) is discussed and characterized by stochastic Hamilton system.

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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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