Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise
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| Format: | Preprint |
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2025
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| author | Antunes, Felipe J. P. Saporito, Yuri F. Jaimungal, Sebastian |
| author_facet | Antunes, Felipe J. P. Saporito, Yuri F. Jaimungal, Sebastian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise Antunes, Felipe J. P. Saporito, Yuri F. Jaimungal, Sebastian Machine Learning Computational Finance Mathematical Finance 49N80, 68T07, 65C30 G.1.6; G.3; I.2.6 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. |
| title | Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise |
| topic | Machine Learning Computational Finance Mathematical Finance 49N80, 68T07, 65C30 G.1.6; G.3; I.2.6 |
| url | https://arxiv.org/abs/2512.14967 |