Since January 2024, the German Academic Exchange Service (DAAD) has been supporting the project “A Robust Data Analytics-based FBSDE Solver for High-dimensional Stochastic Control Problem (ACROSS)”, led by Long Teng, Chair of Applied and Computational Mathematics at the University of Wuppertal. The project is funded under the DAAD joint program with the University Grants Committee (UGC) in Hong Kong, in collaboration with Phillip Yam’s research group in the Department of Statistics at the Chinese University of Hong Kong (CUHK).
The project focuses on developing data analytics-based methods for stochastic control problems in finance – an area where uncertainty and complexity pose major analytical and computational challenges.
Scientific Focus
Uncertainty is inherent in most real-world systems, which are often mathematically modeled as stochastic control systems. In such systems, the goal is to determine an optimal control strategy a decision rule that maximizes the expected outcome while satisfying given constraints. These control problems arise in many fields, particularly in finance.
Only certain classes of control problems admit closed-form analytical solutions. For most others, numerical methods are required. However, conventional numerical approaches often suffer from the curse of dimensionality, making them impractical for high-dimensional systems.
To address this challenge, control problems can be reformulated as backward stochastic differential equations (BSDEs). Recent advances in deep learning-based numerical solvers for BSDEs have shown remarkable potential in handling high-dimensional cases efficiently, thereby mitigating the curse of dimensionality.
Scientific Exchange
A central objective of the ACROSS project is to foster international collaboration among young researchers. This goal has been achieved with great success through a series of bilateral workshops and research visits.
The following image captures a presentation by an early-career researcher during the University of Wuppertal team’s visit to Hong Kong, exemplifying the dynamic exchange of ideas between the two teams.
The Final Phase
The project has advanced very successfully, meeting several of its key research objectives. Multiple learning-based BSDE solvers have been developed and published in academic journals,representing significant progress in this field.
Moreover, several junior scientists have gained valuable international experience through research stays at the partner universities.
As the project enters its final phase, it will formally conclude with a workshop in Wuppertal in December 2025, coinciding with the visit of the Hong Kong team. This concluding event will provide a platform to showcase the project’s achievements and explore future directions for joint research between the German and Hong Kong teams.