Enforcing asymptotic behavior with DNNs for approximation and regression in finance

TL;DR

This paper introduces a straightforward method to incorporate specific asymptotic behaviors into deep neural network approximations, improving accuracy and convergence in finance-related function approximation and regression tasks.

Contribution

It presents a flexible, easy-to-implement approach to enforce asymptotic behavior in DNNs, applicable to various behaviors and dimensions, demonstrated on linear asymptotics.

Findings

Enforcing asymptotic behavior improves approximation accuracy.

The method leads to faster convergence in training.

Applicable to both function and derivative approximation.

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.