Type \(G\) and spherical distributions on \(\mathbb R^d\)
type: Item
instance of: scholarly article
title: Type \(G\) and spherical distributions on \(\mathbb R^d\)
zbMATH Open document ID: 1067.62055
author: Stergios Fotopoulos
published in: Statistics \& Probability Letters
publication date: 2005-05-12T00:00:00Z
review text: It is well-known that the normality assumption for the return distribution is contravened in various important concrete situations (time series data, option prices, etc.). A solution to this status was the introduction and use of the type G family of processes as a suitable subclass of Lévy processes that allows retaining some of the Gaussian properties of the traditional Wiener process and yet to remain rich enough to incorporate processes with jumps and infinite variance. The purpose of this paper is to devise an exact convenient representation of type G distributions, provided that they are of spherical kind, and to investigate basic properties and examples of the proposed representation. The considered methodology of representing type G distributions reveals new mechanisms in extracting families of distributions that supply an insightful understanding of various applications in mathematical and computational finance. Three different examples are bestowed to illustrate and enrich the proposed method.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 91B28
zbMATH DE Number: 2167366
zbMATH Keywords: return distribution
zbMATH Keywords: type G family of processes
zbMATH Keywords: Lévy process
zbMATH Keywords: Lévy measures
zbMATH Keywords: processes with jumps and infinite variance
zbMATH Keywords: variance mixtures of normal distributions
zbMATH Keywords: radial functions
zbMATH Keywords: series and integral representations
zbMATH Keywords: mathematical and computational finance
MaRDI profile type: Publication
full work available at URL: j.spl.2004.11.022
OpenAlex ID: W2039393954
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DOI: 10.1016/J.SPL.2004.11.022
description: scientific article; zbMATH DE number 2167366