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The paper uses neural networks and a path-wise loss derived from elicitability to solve McKean-Vlasov FBSDEs with common noise, avoiding nested Monte Carlo simulation. For ML readers, the useful part is the training-objective design: it shows how scoring rules can make conditional expectations learnable, with validation against analytical solutions in a systemic-risk model. The applications are in mathematical finance and mean-field games, so the evidence for broader use is still narrow.
Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise
arXiv:2512.14967v3 Announce Type: replace 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 hybrid feedforward and recurrent 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.
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 hybrid feedforward and recurrent 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.
Machine Learning (cs.LG); Computational Finance (q-fin.CP); Mathematical Finance (q-fin.MF)
G.1.6; G.3; I.2.6
arXiv:2512.14967 [cs.LG]
(or arXiv:2512.14967v3 [cs.LG] for this version)
From: Yuri F. Saporito [view email] [v1] Tue, 16 Dec 2025 23:39:31 UTC (366 KB) [v2] Thu, 11 Jun 2026 18:54:39 UTC (514 KB) [v3] Sat, 10 Oct 2026 13:19:09 UTC (530 KB)
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