General Financial Modelling

Enforcing asymptotic behavior with DNNs for approximation and regression in finance ArXiv ID: 2411.05257 “View on arXiv” Authors: Unknown 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. ...

Student t-Lévy regression model in YUIMA ArXiv ID: 2403.12078 “View on arXiv” Authors: Unknown Abstract The aim of this paper is to discuss an estimation and a simulation method in the \textsf{“R”} package YUIMA for a linear regression model driven by a Student-$t$ Lévy process with constant scale and arbitrary degrees of freedom. This process finds applications in several fields, for example finance, physic, biology, etc. The model presents two main issues. The first is related to the simulation of a sample path at high-frequency level. Indeed, only the $t$-Lévy increments defined on an unitary time interval are Student-$t$ distributed. In YUIMA, we solve this problem by means of the inverse Fourier transform for simulating the increments of a Student-$t$ Lévy defined on a interval with any length. A second problem is due to the fact that joint estimation of trend, scale, and degrees of freedom does not seem to have been investigated as yet. In YUIMA, we develop a two-step estimation procedure that efficiently deals with this issue. Numerical examples are given in order to explain methods and classes used in the YUIMA package. ...