Mathematical Foundations of Regression Methods for the approximation of the Forward Initial Margin
Abundant literature has been published on approximation methods for the forward initial margin. The most popular ones being the family of regression methods. This paper describes the mathematical foundations on which these regression approximation methods lie. We introduce mathematical rigor to show that in essence, all the methods propose variations of approximations for the conditional expectation function, which is interpreted as an orthogonal projection on Hilbert spaces. We show that each method is simply choosing a different functional form to numerically estimate the conditional expectation. We cover in particular the most popular methods in the literature so far, Polynomial approximation, Kernel regressions and Neural Networks.
Code (0)
등록된 구현이 없습니다.
Tasks
regressionSimilar Papers 제목 키워드 기반
Approximation Power of Deep Neural Networks: an explanatory mathematical survey
This survey provides an in-depth and explanatory review of the approximation properties of deep neural networks, with a focus on feed-forward and residual architectures. The primary objective is to examine how effectivel…
SurveyTensor-Based Foundations of Ordinary Least Squares and Neural Network Regression Models
This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By lever…
Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differe…
Error Propagation in Dynamic Programming: From Stochastic Control to Option Pricing
This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing t…
Mathematical Foundations of Deep Learning
This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural net…
Reinforcement Learning