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"Asymptotic Expansions as Control Variates for Deep Solvers to Fully-coupled Forward-backward Stochastic Differential Equations" Abstract Coupled forward-backward stochastic differential equations (FBSDEs) are closely related to financially important issues such as optimal investment. However, it is well known that obtaining solutions is challenging, even when employing numerical methods. In this paper, we propose new methods that combine an algorithm recently developed for coupled FBSDEs and an asymptotic expansion approach to those FBSDEs as control variates for learning of the neural networks. The proposed method is demonstrated to perform better than the original algorithm in numerical examples, including one with a financial implication. The results show that the proposed method exhibits not only faster convergence but also greater stability in computation

Author

Listed:
  • Makoto Naito

    (School of Management, Tokyo Metropolitan University)

  • Taiga Saito

    (School of Commerce, Senshu University)

  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

  • Kohta Takehara

    (School of Management, Tokyo Metropolitan University)

Abstract

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  • Makoto Naito & Taiga Saito & Akihiko Takahashi & Kohta Takehara, 2025. ""Asymptotic Expansions as Control Variates for Deep Solvers to Fully-coupled Forward-backward Stochastic Differential Equations" Abstract Coupled forward-backward stochastic differential equ," CIRJE F-Series CIRJE-F-1245, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2025cf1245
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