78310

Автор(ы): 

Автор(ов): 

1

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

On Properties of the Hyperbolic Distribution

ISBN/ISSN: 

2227-7390

DOI: 

10.3390/math12182888

Наименование источника: 

  • Mathematics

Обозначение и номер тома: 

Т. 12, вып. 18:2888

Город: 

  • Базель, Швейцария

Издательство: 

  • MDPI

Год издания: 

2024

Страницы: 

https://www.mdpi.com/2227-7390/12/18/2888
Аннотация
This paper is set to analytically describe properties of the hyperbolic distribution. This law, along with the variance-gamma distribution, is one of the most popular normal mean–variance mixtures from the point of view of various applications. We have found closed form expressions for the cumulative distribution and partial moment-generating functions of the hyperbolic distribution. The obtained formulas use the values of the Humbert confluent hypergeometric and Whittaker special functions. The results are applied to the problem of European option pricing in the related Levy model of financial market. The research demonstrates that the discussed normal mean–variance mixture is analytically tractable.

Библиографическая ссылка: 

Иванов Р.В. On Properties of the Hyperbolic Distribution // Mathematics. 2024. Т. 12, вып. 18:2888. С. https://www.mdpi.com/2227-7390/12/18/2888.