相关正态随机变量乘积分布的渐近近似值

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-11-05 DOI:10.1016/j.jmaa.2024.128987

Robert E. Gaunt, Zixin Ye

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引用次数: 0

摘要

我们获得了具有非零均值和任意方差的两个相关正态随机变量乘积的概率密度函数的渐近近似值。因此，我们推导出了该分布的尾概率和量子函数的渐近近似值，以及广泛使用的风险度量值和尾风险值的渐近近似值。

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Asymptotic approximations for the distribution of the product of correlated normal random variables

We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the tail probabilities and quantile functions of this distribution, as well as an asymptotic approximation for the widely used risk measures value at risk and tail value at risk.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.