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

• URL: http://arxiv.org/abs/2512.14967v1
• Date: Tue, 16 Dec 2025 23:39:31 GMT
• Title: Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise
• Authors: Felipe J. P. Antunes, Yuri F. Saporito, Sebastian Jaimungal,
• Abstract summary: We present a novel numerical method for solving McKean-Vlasov forward-backward differential equations (MV-FBSDEs) with common noise.<n>The key innovation involves elicitability to derive a path-wise loss function, enabling efficient training of neural networks to approximate both the backward process and the conditional expectations arising from common noise.<n>We validate the algorithm on a systemic risk inter-bank borrowing and lending model, where analytical solutions exist, demonstrating accurate recovery of the true solution.
• Score: 2.421459418045937
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We present a novel numerical method for solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves elicitability to derive a path-wise loss function, enabling efficient training of neural networks to approximate both the backward process and the conditional expectations arising from common noise - without requiring computationally expensive nested Monte Carlo simulations. The mean-field interaction term is parameterized via a recurrent neural network trained to minimize an elicitable score, while the backward process is approximated through a feedforward network representing the decoupling field. We validate the algorithm on a systemic risk inter-bank borrowing and lending model, where analytical solutions exist, demonstrating accurate recovery of the true solution. We further extend the model to quantile-mediated interactions, showcasing the flexibility of the elicitability framework beyond conditional means or moments. Finally, we apply the method to a non-stationary Aiyagari--Bewley--Huggett economic growth model with endogenous interest rates, illustrating its applicability to complex mean-field games without closed-form solutions.

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