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Enforcing asymptotic behavior with DNNs for approximation and regression in finance

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  • Hardik Routray
  • Bernhard Hientzsch

Abstract

We propose a simple methodology to approximate functions with given asymptotic behavior by specifically constructed terms and an unconstrained deep neural network (DNN). The methodology we describe extends to various asymptotic behaviors and multiple dimensions and is easy to implement. In this work we demonstrate it for linear asymptotic behavior in one-dimensional examples. We apply it to function approximation and regression problems where we measure approximation of only function values (``Vanilla Machine Learning''-VML) or also approximation of function and derivative values (``Differential Machine Learning''-DML) on several examples. We see that enforcing given asymptotic behavior leads to better approximation and faster convergence.

Suggested Citation

  • Hardik Routray & Bernhard Hientzsch, 2024. "Enforcing asymptotic behavior with DNNs for approximation and regression in finance," Papers 2411.05257, arXiv.org.
    • Handle: RePEc:arx:papers:2411.05257
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    References listed on IDEAS

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    1. Bernhard Hientzsch, 2019. "Introduction to Solving Quant Finance Problems with Time-Stepped FBSDE and Deep Learning," Papers 1911.12231, arXiv.org.
    2. Arun Kumar Polala & Bernhard Hientzsch, 2023. "Parametric Differential Machine Learning for Pricing and Calibration," Papers 2302.06682, arXiv.org, revised Feb 2023.
    3. Ali Fathi & Bernhard Hientzsch, 2023. "A Comparison of Reinforcement Learning and Deep Trajectory Based Stochastic Control Agents for Stepwise Mean-Variance Hedging," Papers 2302.07996, arXiv.org, revised Nov 2023.
    4. Yajie Yu & Narayan Ganesan & Bernhard Hientzsch, 2023. "Backward Deep BSDE Methods and Applications to Nonlinear Problems," Risks, MDPI, vol. 11(3), pages 1-16, March.
    5. Bernhard Hientzsch, 2023. "Reinforcement Learning and Deep Stochastic Optimal Control for Final Quadratic Hedging," Papers 2401.08600, arXiv.org.
    6. Arun Kumar Polala & Bernhard Hientzsch, 2024. "A case study on different one-factor Cheyette models for short maturity caplet calibration," Papers 2408.11257, arXiv.org.
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