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Deep high-order splitting method for semilinear degenerate PDEs and application to high-dimensional nonlinear pricing models

Author

Listed:
  • Riu Naito

    (Hitotsubashi University & Japan Post Insurance Co., Ltd.)

  • Toshihiro Yamada

    (Hitotsubashi University)

Abstract

The paper introduces a new deep learning-based high-order discretization method for semilinear degenerate parabolic partial differential equations based on a Gaussian Kusuoka approximation and shows its application to finance. The proposed deep learning-based algorithm for solving high-dimensional nonlinear problems is efficiently implemented without suffering from the curse of dimensionality. We show numerical examples for high-dimensional (100- and 150-dimensional) nonlinear pricing models and check the effectiveness of the proposed method.

Suggested Citation

  • Riu Naito & Toshihiro Yamada, 2024. "Deep high-order splitting method for semilinear degenerate PDEs and application to high-dimensional nonlinear pricing models," Digital Finance, Springer, vol. 6(4), pages 693-725, December.
    • Handle: RePEc:spr:digfin:v:6:y:2024:i:4:d:10.1007_s42521-023-00091-z
    DOI: 10.1007/s42521-023-00091-z
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Semilinear PDEs; Deep learning; Gaussian Kusuoka approximation; High-dimensional financial diffusions; CVA;
    All these keywords.

    JEL classification:

    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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