论双曲线分布的性质

IF 2.3 3区数学 Q1 MATHEMATICS

Mathematics Pub Date : 2024-09-16 DOI:10.3390/math12182888

Roman V. Ivanov

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引用次数: 0

摘要

本文旨在分析描述双曲线分布的特性。从各种应用的角度来看，该定律与方差-伽马分布是最常用的正态均方差混合物之一。我们找到了双曲线分布的累积分布和部分动量生成函数的封闭式表达式。所获得的公式使用了亨伯特汇合双曲函数和惠特克特殊函数的值。研究结果被应用于金融市场相关莱维模型中的欧式期权定价问题。研究表明，所讨论的正态均值-方差混合物在分析上是可行的。

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On Properties of the Hyperbolic Distribution

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 Lévy model of financial market. The research demonstrates that the discussed normal mean–variance mixture is analytically tractable.

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来源期刊

Mathematics Mathematics-General Mathematics

CiteScore

4.00

自引率

16.70%

发文量

4032

审稿时长

21.9 days

期刊介绍： Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.