JOURNAL ARTICLE

Deep Quadratic Hedging.

  • Published In: Mathematics of Operations Research (INFORMS), 2025, v. 50, n. 4. P. 2972 1 of 3

  • Database: Business Source Ultimate 2 of 3

  • Authored By: Gnoatto, Alessandro; Lavagnini, Silvia; Picarelli, Athena 3 of 3

Abstract

This article presents a novel computational methodology for quadratic hedging in high-dimensional incomplete financial markets, focusing on mean-variance hedging and local risk minimization. Both approaches are reformulated as backward stochastic differential equations (BSDEs), which are then solved using a deep learning–based BSDE solver to overcome the curse of dimensionality. The method is tested on a multidimensional extension of the Heston stochastic volatility model, demonstrating high accuracy in pricing and hedging, including in settings with up to 100 underlying assets where traditional PDE methods become infeasible. The paper also provides theoretical results on existence and uniqueness for the associated stochastic Riccati equations and discusses convergence properties of the deep solver, positioning this approach as a scalable tool for risk management in complex financial markets.

Additional Information

  • Source:Mathematics of Operations Research (INFORMS). 2025/11, Vol. 50, Issue 4, p2972
  • Document Type:Article
  • Subject Area:Business and Management
  • Publication Date:2025
  • ISSN:0364-765X
  • DOI:10.1287/moor.2023.0213
  • Accession Number:189423740
  • Copyright Statement:Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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