arXiv subjects

Rundong Xu

Publications and source records attributed to Rundong Xu.

7 recordsLinked to original sources

arXiv2025

Global Convergence of Successive Approximations for Non-convex Stochastic Optimal Control Problems

This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The control-dependent diffusions make the traditional method of successive approximations (MSA) insufficient to reduce the value of cost functional in each iteration. Without adding extra terms over which to perform the Hamiltonian minimization, the MSA becomes sufficient by our novel error estimate involving a higher order backward adjoint equation. Under certain convexity assumptions on the coefficients (no convexity assumptions on the control domains), the value of the cost functional descends to the global minimum as the number of iterations tends to infinity. In particular, a convergence rate is available for a class of generalized linear-quadratic systems.

math.OC↗

arXiv2025

A BSDE approach to the asymmetric risk-sensitive optimization and its applications

This paper is devoted to proposing a new asymmetric risk-sensitive criterion involving different risk attitudes toward varying risk sources. The criterion can only be defined through the initial value of the minimal solutions of quadratic backward stochastic differential equations (BSDEs). Before uncovering the mean-variance representation for the introduced criterion by the variational approach, some axioms are given for the first time to characterize a variance decomposition of square integrable random variables. The stochastic control problems under this criterion are described as a kind of stochastic recursive control problems that includes controlled quadratic BSDEs. An asymmetric risk-sensitive global stochastic maximum principle is derived when the quadratic BSDEs are equipped with bounded data. A closed-form solution of a stochastic linear-quadratic risk-sensitive control problem is obtained by introducing a novel completion-of-squares technique for controlled quadratic BSDEs. In addition, a dynamic portfolio optimization problem featuring a stochastic return rate is provided as an application of the asymmetric risk-sensitive control.

math.OC↗

arXiv2025

A quadratic BSDE approach to normalization for the finite volume 2D sine-Gordon model in the finite ultraviolet regime

This paper is devoted to a new construction of the two-dimensional sine-Gordon model on bounded domains by a novel normalization technique in the finite ultraviolet regime. Our methodology involves a family of backward stochastic differential equations (BSDEs for short) driven by a cylindrical Wiener process, whose generators are purely quadratic functions of the second unknown variable. The terminal conditions of the quadratic BSDEs are uniformly bounded and converge in probability to the real part of imaginary multiplicative chaos tested against an arbitrarily given test function, which helps us describe our sine-Gordon measure through some delicate estimates concerning bounded mean oscillation martingales. As the ultraviolet cutoffs are vanishing, the quadratic BSDEs converge to a quadratic BSDE that completely characterizes the absolute continuity of our sine-Gordon measure with respect to the law of Gaussian free fields. Our approach can also be used effectively to establish the connection between our sine-Gordon measure and the scaling limit of correlation functions of the critical planar XOR-Ising model and to prove the weak convergence of the normalized charge distributions of two-dimensional log-gases.

math.PR↗

arXiv2023

A Stochastic Maximum Principle for Forward-backward Stochastic Control Systems with Quadratic Generators and Sample-wise Constraints

This paper examines the stochastic maximum principle (SMP) for a forward-backward stochastic control system where the backward state equation is characterized by the backward stochastic differential equation (BSDE) with quadratic growth and the forward state at the terminal time is constrained in a convex set with probability one. With the help of the theory of BSDEs with quadratic growth and the bounded mean oscillation (BMO) martingales, we employ the terminal perturbation approach and Ekeland's variational principle to obtain a dynamic stochastic maximum principle. The main result has a wide range of applications in mathematical finance and we investigate a robust recursive utility maximization problem with bankruptcy prohibition as an example.

math.OC↗

arXiv2023

The space cold atom interferometer for testing the equivalence principle in the China Space Station

The precision of the weak equivalence principle (WEP) test using atom interferometers (AIs) is expected to be extremely high in microgravity environment. The microgravity scientific laboratory cabinet (MSLC) in the China Space Station (CSS) can provide a higher-level microgravity than the CSS itself, which provides a good experimental environment for scientific experiments that require high microgravity. We designed and realized a payload of a dual-species cold rubidium atom interferometer. The payload is highly integrated and has a size of 460 mm * 330 mm * 260 mm. It will be installed in the MSLC to carry out high-precision WEP test experiment. In this article, we introduce the constraints and guidelines of the payload design, the compositions and functions of the scientific payload, the expected test precision in space, and some results of the ground test experiments

physics.atom-ph↗

arXiv2022

A Modified Method of Successive Approximations for Stochastic Recursive Optimal Control Problems

Based on the stochastic maximum principle for the partially coupled forward-backward stochastic control system (FBSCS for short), a modified method of successive approximations (MSA for short) is established for stochastic recursive optimal control problems. The second-order adjoint processes are introduced in the augmented Hamiltonian minimization step since the control domain is not necessarily convex. Thanks to the theory of bounded mean oscillation martingales (BMO martingales for short), we give a delicate proof of the error estimate and then prove the convergence of the modified MSA algorithm. In a special case, we obtain a logarithmic convergence rate. When the control domain is convex and compact, a sufficient condition which makes the control returned from the MSA algorithm be a near-optimal control is given for a class of linear FBSCSs.

math.OC↗

arXiv2021

A Global Stochastic Maximum Principle for Forward-Backward Stochastic Control Systems with Quadratic Generators

We study a stochastic optimal control problem for forward-backward control systems with quadratic generators. In order to establish the first and second-order variational and adjoint equations, we obtain a new estimate for one-dimensional linear BSDEs with unbounded stochastic Lipschitz coefficients involving bounded mean oscillation martingales (BMO-martingales for short) and prove the solvability for a class of multi-dimensional BSDEs with this type. Finally, a new global stochastic maximum principle is deduced.

math.OC↗