Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise

arXiv — cs.LGThursday, December 18, 2025 at 5:00:00 AM
  • A novel numerical method has been introduced for solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) with common noise, utilizing deep learning and elicitability to create an efficient training framework for neural networks. This method avoids the need for costly nested Monte Carlo simulations by deriving a path-wise loss function and approximating the backward process through a feedforward network.
  • This development is significant as it enhances the accuracy and efficiency of modeling systemic risk in financial systems, particularly in inter-bank borrowing and lending scenarios. The validation of this algorithm against known analytical solutions demonstrates its potential for practical applications in finance and economics.
  • The integration of deep learning techniques into stochastic differential equations reflects a broader trend in artificial intelligence, where traditional mathematical approaches are being augmented by machine learning. This shift not only addresses computational challenges but also opens new avenues for research in high-dimensional problems, as seen in other recent advancements in deep learning methodologies across various applications.
— via World Pulse Now AI Editorial System

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