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Mathematics
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Stochastic Optimal Control, Game Theory, and Related Applications
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Stochastic Optimal Control, Game Theory, and Related Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 20 August 2025 | Viewed by 1228

Special Issue Editors

Prof. Dr. Tianyang Nie

E-Mail Website
Guest Editor
School of Mathematics, Shandong University, Jinan 250100, China
Interests: stochastic control; mean-field games; mathematical finance; backward stochastic differential equations
Prof. Dr. Qi Zhang

E-Mail Website
Guest Editor
Laboratory of Mathematics for Nonlinear Science, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
Interests: forward backward stochastic differential equations; stochastic control; stochastic analysis
Dr. Shujun Wang

E-Mail Website
Guest Editor
School of Management, Shandong University, Jinan 250100, China
Interests: stochastic control; mean-field games; forward backward stochastic differential equations

Special Issue Information

Dear Colleagues,

Stochastic optimal control and game theory have a strong mathematical foundation and have important applications in science, technology, and society. To better characterize models in real applications, we need to consider control and game problems for complex stochastic systems, including constrained stochastic systems, mean field systems, recursive systems, discrete time systems, etc. Considering the importance, universality, and rapid development of stochastic control and game theory, this Special Issue illustrates how to obtain the optimal control/strategy for complex stochastic systems and design the optimal decisions for practical optimization problems. This Special Issue will be a practical reference on mathematical approaches to stochastic optimal control and game theory, while also providing models and tools for solving practical problems. It will appeal to a broad audience interested in the general field of mathematical control theory and engineering control theory. This Special Issue aims to focus on frontier advances in the field of stochastic optimal control and game theory for different kinds of systems, as well as related applications in engineering and finance.

Prof. Dr. Tianyang Nie
Prof. Dr. Qi Zhang
Dr. Shujun Wang
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • stochastic optimal control
  • game theory
  • maximum principle
  • dynamic programming principle
  • forward–backward differential equations
  • HJB equations

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Published Papers (3 papers)

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18 pages, 369 KiB  
Article
Backward Stochastic Linear Quadratic Optimal Control with Expectational Equality Constraint
by Yanrong Lu, Jize Li and Yonghui Zhou
Mathematics 2025, 13(8), 1327; https://doi.org/10.3390/math13081327 - 18 Apr 2025
Viewed by 65
Abstract
This paper investigates a backward stochastic linear quadratic control problem with an expected-type equality constraint on the initial state. By using the Lagrange multiplier method, the problem with a uniformly convex cost functional is first transformed into an equivalent unconstrained parameterized backward stochastic [...] Read more.
This paper investigates a backward stochastic linear quadratic control problem with an expected-type equality constraint on the initial state. By using the Lagrange multiplier method, the problem with a uniformly convex cost functional is first transformed into an equivalent unconstrained parameterized backward stochastic linear quadratic control problem. Then, under the surjectivity of the linear constraint, the equivalence between the original problem and the dual problem is proven by Lagrange duality theory. Subsequently, with the help of the maximum principle, an explicit solution of the optimal control for the unconstrained problem is obtained. This solution is feedback-based and determined by an adjoint stochastic differential equation, a Riccati-type ordinary differential equation, a backward stochastic differential equation, and an equality, thereby yielding the optimal control for the original problem. Finally, an optimal control for an investment portfolio problem with an expected-type equality constraint on the initial state is explicitly provided. Full article
(This article belongs to the Special Issue Stochastic Optimal Control, Game Theory, and Related Applications)
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18 pages, 330 KiB  
Article
Mean-Field Modeling of Green Technology Adoption: A Competition for Incentives
by Luca Grosset and Elena Sartori
Mathematics 2025, 13(5), 691; https://doi.org/10.3390/math13050691 - 20 Feb 2025
Viewed by 271
Abstract
This paper investigates the role of fiscal incentives in promoting the transition to a green economy using a dynamic mean-field game framework. By modeling firms as representative agents undergoing an environmentally sustainable transition, we analyze two distinct types of incentive structure: fixed incentives [...] Read more.
This paper investigates the role of fiscal incentives in promoting the transition to a green economy using a dynamic mean-field game framework. By modeling firms as representative agents undergoing an environmentally sustainable transition, we analyze two distinct types of incentive structure: fixed incentives and incentives based on the average behavior of firms. The findings underscore the importance of balancing incentive structures to avoid economic inefficiencies and ensure a smooth ecological transition. Full article
(This article belongs to the Special Issue Stochastic Optimal Control, Game Theory, and Related Applications)
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27 pages, 414 KiB  
Article
Backward Anticipated Social Optima: Input Constraints and Partial Information
by Shujun Wang
Mathematics 2025, 13(2), 306; https://doi.org/10.3390/math13020306 - 18 Jan 2025
Viewed by 567
Abstract
A class of stochastic linear-quadratic (LQ) dynamic optimization problems involving a large population is investigated in this work. Here, the agents cooperate with each other to minimize certain social costs. Furthermore, differently from the classic social optima literature, the dynamics in this framework [...] Read more.
A class of stochastic linear-quadratic (LQ) dynamic optimization problems involving a large population is investigated in this work. Here, the agents cooperate with each other to minimize certain social costs. Furthermore, differently from the classic social optima literature, the dynamics in this framework are driven by anticipated backward stochastic differential equations (ABSDE) in which the terminal instead of the initial condition is specified and the anticipated terms are involved. The individual admissible controls are constrained in closed convex subsets, and the common noise is considered. As a result, the related social cost is represented by a recursive functional in which the initial state is involved. By virtue of the so-called anticipated person-by-person optimality principle, a decentralized strategy can be derived. This is based on a class of new consistency condition systems, which are mean-field-type anticipated forward-backward stochastic differential delay equations (AFBSDDEs). The well-posedness of such a consistency condition system is obtained through a discounting decoupling method. Finally, the corresponding asymptotic social optimality is proved. Full article
(This article belongs to the Special Issue Stochastic Optimal Control, Game Theory, and Related Applications)
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