Enforcing asymptotic behavior with DNNs for approximation and regression in finance
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912469167898624 |
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| author | Routray, Hardik Hientzsch, Bernhard |
| author_facet | Routray, Hardik Hientzsch, Bernhard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enforcing asymptotic behavior with DNNs for approximation and regression in finance Routray, Hardik Hientzsch, Bernhard Computational Finance Numerical Analysis Pricing of Securities 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. |
| title | Enforcing asymptotic behavior with DNNs for approximation and regression in finance |
| topic | Computational Finance Numerical Analysis Pricing of Securities |
| url | https://arxiv.org/abs/2411.05257 |