{"ID":2828719,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.14967","arxiv_id":"2512.14967","title":"Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise","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.","short_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 neur...","url_abs":"https://arxiv.org/abs/2512.14967","url_pdf":"https://arxiv.org/pdf/2512.14967v1","authors":"[\"Felipe J. P. Antunes\",\"Yuri F. Saporito\",\"Sebastian Jaimungal\"]","published":"2025-12-16T23:39:31Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"q-fin.CP\",\"q-fin.MF\"]","methods":"[]","has_code":false}