arXiv subjects

Jiaqiang Wen

Publications and source records attributed to Jiaqiang Wen.

At least 19 recordsLinked to original sources

arXiv2026

A global stochastic maximum principle for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition

In this paper, we study a stochastic optimal control problem for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition, where the control domain is not necessarily convex. Due to the absence of bounded mean oscillation (BMO) martingales approach, we introduce a new probability measure, under which all subsequent analysis is then carried out under this new measure. Finally, by means of a new approach to the derivation of the adjoint equations, a global stochastic maximum principle is established.

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arXiv2026

Sharp propagation of chaos for mean-field backward stochastic differential equations

We study propagation of chaos for decoupled mean-field forward-backward stochastic differential equations whose generators depend on the empirical laws of the forward states, backward values and diagonal martingale integrands. Under monotonicity and Lipschitz assumptions, synchronous coupling gives quantitative estimates, including an $m$-particle squared Wasserstein bound of order $m/n$ for a system of $n$ particles interacting through finitely many statistics. In the Markovian setting, assuming a sufficiently regular classical decoupling field, we obtain two sharp refinements. For constant invertible diffusion and first-order cancellation of the field's measure dependence along the limiting law flow, the squared Wasserstein error is of order $m^2/n^2$, on continuous-path space for the values and on $L^2$ for the diagonal integrands. Without imposing this cancellation, smooth weak errors have order $n^{-1}$ for every fixed marginal, allowing variable and possibly degenerate diffusion. The weak estimate is uniform on a fixed time interval for the values and integrated in time for the integrands. The argument compares the interacting BSDE with an empirical evaluation of the decoupling field, retaining the full martingale representation and controlling feedback through both backward laws. It yields a joint-path Wasserstein transfer bound with intrinsic squared error $m/n^2$, off-diagonal integrand estimates, and a weak-error transfer principle with additive error $n^{-1}$. Explicit models with feedback through both backward laws verify the cancellation assumptions. Examples distinguish the intrinsic backward error from the forward law error and establish matching lower bounds for each backward component.

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arXiv2026

Backward doubly stochastic differential equations with or without reflection under weak conditions

In this paper, we study the solvability of backward doubly stochastic differential equations (BDSDEs, for short), both with and without reflection, under weak conditions on the generator. First, when the generator $f$ is of general growth in $y$ and linear growth in $z$, we establish the existence, uniqueness, comparison principle, and the existence of maximal solutions. Second, when $f$ is of linear growth in $y$ and quadratic growth in $z$ with bounded terminal value, we prove the existence, uniqueness, and comparison principle. Finally, when $f$ is of general growth in $y$ and quadratic growth in $z$ with bounded terminal value, we prove the existence of maximal solutions.

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arXiv2026

Indefinite Stochastic Linear-Quadratic Optimal Control Problems with Random Coefficients and Poisson Jumps: Closed-Loop Representation of Open-Loop Optimal Controls

This paper is concerned with stochastic linear-quadratic (SLQ) optimal control problems with random coefficients and Poisson jumps. The weighting matrices are allowed to be random and indefinite. Under the uniform convexity condition, the global fundamental matrix representation $P=\mathbf Y\mathbf X^{-1}$, used in the diffusion case, is generally unavailable because Poisson jumps may cause the optimal state fundamental matrix $\mathbf X$ to become singular. We construct the process $P$ directly from the stochastic value flow and prove that the associated stochastic Riccati equation with jumps (SRE-J) admits a unique maximal strongly regular solution, which gives a closed-loop representation of the unique open-loop optimal control. We also give sufficient conditions for uniform convexity and present indefinite SLQ examples with jumps.

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arXiv2026

Near optimal controls for partially observed stochastic linear quadratic problems

In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the diffusion term of the state equation, the circular dependence between the control process and the filtration generated by the observation, and the observation process contains an unbounded drift term. We address these difficulties by first restricting the control to a smaller domain, which enables us to apply the Girsanov theorem using a conditional argument and thereby break the circular dependence. Subsequently, we study the restricted problem using a non-standard variation method. The desired near optimal control is then obtained by taking the limit of an approximating sequence.

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arXiv2026

Quadratic Mean-Field BSDEs and Exponential Utility Maximization

In this paper, we study a class of real-valued mean-field backward stochastic differential equations (BSDEs) with generators of quadratic growth in the control variable and the mean-field term. Under this assumption, together with a bounded terminal condition, we establish the existence and uniqueness of solutions. Our approach departs from classical fixed-point arguments and instead combines Malliavin calculus with refined BMO and stability estimates. The result bridges the gap between the quadratic BSDE results of [Ann. Probab. 45 (2017), pp.~3795--3828] and Hao et al. [Ann. Appl. Probab. 35 (2025), pp.~2128--2174]. Moreover, motivated by the structure of the mean-field exponential utility maximization problem introduced in our paper, we extend our framework to terminal conditions without continuity or the Markovian assumption. We establish the existence and uniqueness of solutions under a smallness terminla value on the terminal conditions. We then apply this extended theory to solve a mean-field exponential utility maximization problem, which developing the classical framework of Hu et al. [Ann. Appl. Probab. 15 (2005), pp.~1691--1712] to a fully coupled quadratic mean-field setting.

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arXiv2025

Mean-field backward stochastic Volterra integral equations: well-posedness and related particle system

This paper studies the mean-field backward stochastic Volterra integral equations (mean-field BSVIEs) and associated particle systems. We establish the existence and uniqueness of solutions to mean-field BSVIEs when the generator $g$ is of linear growth or quadratic growth with respect to $Z$, respectively. Moreover, the propagation of chaos is analyzed for the corresponding particle systems under two conditions. When $g$ is of linear growth in $Z$, the convergence rate is proven to be of order $\mathscr{Q}(N)$. When $g$ is of quadratic growth in $Z$ and is independent of the law of $Z$, we not only establish the convergence of the particle systems but also derive a convergence rate of order $\mathscr{O}(N^{-\frac{1}{2λ}})$, where $λ>1$.

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arXiv2025

Multi-dimensional anticipated backward stochastic differential equations with quadratic growth

This paper is devoted to the general solvability of anticipated backward stochastic differential equations with quadratic growth by relaxing the assumptions made by Hu, Li, and Wen \cite[Journal of Differential Equations, 270 (2021), 1298--1311]{hu2021anticipated} from the one-dimensional case with bounded terminal values to the multi-dimensional situation with bounded/unbounded terminal values. Three new results regarding the existence and uniqueness of local and global solutions are established. More precisely, for the local solution with bounded terminal values, the generator $f(t, Y_t, Z_t, Y_{t+δ_t},Z_{t+ζ_t})$ is of general growth with respect to $Y_t$ and $Y_{t+δ_{t}}$. For the global solution with bounded terminal values, the generator $f(t, Y_t, Z_t, Y_{t+δ_t},Z_{t+ζ_t})$ is of skew sub-quadratic but also ``strictly and diagonally" quadratic growth in $Z_t$. For the global solution with unbounded terminal values, the generator $f(t, Y_t, Z_t, Y_{t+δ_t})$ is of diagonal quadratic growth in $Z_t$ in the first case; and in the second case, the generator $f(t, Z_t)$+$E[g(t, Y_t,Z_t, Y_{t+δ_t},Z_{t+ζ_t})]$ is of diagonal quadratic growth in $Z_t$ and linear growth in $Z_{t+ζ_t}$.

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arXiv2025

Maximum Principle of Stochastic Optimal Control Problems with Model Uncertainty

This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching. Firstly, the $ L^β$-solutions of forward-backward stochastic differential equations with regime switching are given. Secondly, we obtain the variational inequality by making use of the continuity of solutions to variational equations with respect to the uncertainty parameter $θ$. Thirdly, utilizing the linearization and weak convergence techniques, we prove the necessary stochastic maximum principle and provide sufficient conditions for the stochastic optimal control. Finally, as an application, a risk-minimizing portfolio selection problem is studied.

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arXiv2024

Mean-field backward stochastic differential equations and nonlocal PDEs with quadratic growth

In this paper, we study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and global solutions are proved with some new ideas for a one-dimensional mean-field BSDE when the generator $g\big(t, Y, Z, \mathbb{P}_{Y}, \mathbb{P}_{Z}\big)$ has a quadratic growth in $Z$ and the terminal value is bounded. Second, a comparison theorem for the general mean-field BSDEs is obtained with the Girsanov transform. Third, we prove the convergence of the particle systems to the mean-field BSDEs with quadratic growth, and the convergence rate is also given. Finally, in this framework, we use the mean-field BSDE to provide a probabilistic representation for the viscosity solution of a nonlocal partial differential equation (PDE, for short) as an extended nonlinear Feynman-Kac formula, which yields the existence and uniqueness of the solution to the PDE.

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arXiv2024

A local maximum principle for robust optimal control problems of quadratic BSDEs

The paper concerns the necessary maximum principle for robust optimal control problems of quadratic BSDEs. The coefficient of the systems depends on the parameter $θ$, and the generator of BSDEs is of quadratic growth in $z$. Since the model is uncertain, the variational inequality is proved by weak convergence technique. In addition, due to the generator being quadratic with respect to $z$, the forward adjoint equations are SDEs with unbounded coefficient involving mean oscillation martingales. Using reverse Hölder inequality and John-Nirenberg inequality, we show that its solutions are continuous with respect to the parameter $θ$. The necessary and sufficient conditions for robust optimal control are proved by linearization method.

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arXiv2023

Dynamic programming principle for delayed stochastic recursive optimal control problem and HJB equation with non-Lipschitz generator

In this paper, we study the delayed stochastic recursive optimal control problem with a non-Lipschitz generator, in which both the dynamics of the control system and the recursive cost functional depend on the past path segment of the state process in a general form. First, the dynamic programming principle for this control problem is obtained. Then, by the generalized comparison theorem of backward stochastic differential equations and the stability of viscosity solutions, we establish the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Finally, an application to the consumption-investment problem under the delayed continuous-time Epstein-Zin utility with a non-Lipschitz generator is presented.

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arXiv2022

A Global Maximum Principle for Controlled Conditional Mean-field FBSDEs with Regime Switching

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 driver of backward stochastic differential equations (BSDEs, for short) could depend on $Z$. Different from the case of non-recursive utility, the first-order and second-order adjoint equations are both high-dimensional linear BSDEs. Based on the adjoint equations, we reveal the relations among the terms of the first- and second-order Taylor's expansions. A general maximum principle is proved, which develops the work of Nguyen, Yin, and Nguyen [22] to recursive utility. As applications, the linear-quadratic problem is considered and a problem with state constraint is studied.

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arXiv2022

Fractional backward stochastic differential equations with delayed generator

In this paper, we focus on the solvability of a class of fractional backward stochastic differential equations (BSDEs, for short) with delayed generator. In this class of equations, the generator includes not only the values of the solutions of the present but also the past. Under Lipschitz condition, the existence and uniqueness of such BSDEs are established. A comparison theorem for this class of BSDEs is also obtained.

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arXiv2022

Large Deviation Principle for Backward Stochastic Differential Equations with a stochastic Lipschitz condition on $z$

In this paper, a probabilistic interpretation for the viscosity solution of a parabolic partial differential equation is obtained by virtue of the solution of a class of quadratic backward stochastic differential equations (BSDEs, for short). Furthermore, we prove the convergence and the large deviation principle for the solution of this class of quadratic BSDEs, which is associated with a family of Markov processes with the diffusion coefficients that tend to be zero.

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arXiv2022

Solvability of a class of mean-field BSDEs with quadratic growth

In this paper, we study the multi-dimensional mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. Under small terminal value, the existence and uniqueness are proved for the multi-dimensional situation when the generator f(t,Y,E[Y],Z,E[Z]) is of quadratic growth with respect to the last four items, using some new methods. Besides, a kind of comparison theorem is obtained.

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arXiv2022

Stochastic Linear Quadratic Optimal Control Problems with Random Coefficients and Markovian Regime Switching System

This paper thoroughly investigates stochastic linear-quadratic optimal control problems with the Markovian regime switching system, where the coefficients of the state equation and the weighting matrices of the cost functional are random. We prove the solvability of the stochastic Riccati equation under the uniform convexity condition and obtain the closed-loop representation of the open-loop optimal control using the unique solvability of the corresponding stochastic Riccati equation. Moreover, by applying Itô's formula with jumps, we get a representation of the cost functional on a Hilbert space, characterized as the adapted solutions of some forward-backward stochastic differential equations. We show that the necessary condition of the open-loop optimal control is the convexity of the cost functional, and the sufficient condition of the open-loop optimal control is the uniform convexity of the cost functional. In addition, we study the properties of the stochastic value flow of the stochastic linear-quadratic optimal control problem. Finally, as an application, we present a continuous-time mean-variance portfolio selection problem and prove its unique solvability.

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arXiv2022

Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs

In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional Itô (or path-dependent) calculus, the relationship between the systems and related path-dependent quasi-linear stochastic partial differential equations (SPDEs in short) is established, and the well-known nonlinear stochastic Feynman-Kac formula of Pardoux and Peng [Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Relat. Fields 98 (1994), pp. 209--227] is developed to the non-Markovian situation. Moreover, we obtain the differentiability of the solution to the forward-backward doubly stochastic systems and some properties of solutions to the path-dependent SPDEs.

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