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

Robert Gaunt; Zixin Ye

doi:10.1016/j.jmaa.2024.128987

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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	128987
Journal	Journal of Mathematical Analysis and Applications
Volume	543
Issue number	2
Early online date	5 Dec 2024
DOIs	https://doi.org/10.1016/j.jmaa.2024.128987
Publication status	Published - 15 Mar 2025

Keywords

Product of correlated normal random variables
probability density function
tail probability
quantile function
tail value at risk
asymptotic approximation

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10.1016/j.jmaa.2024.128987Licence: CC BY

Cite this

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title = "Asymptotic approximations for the distribution of the product of correlated normal random variables",

abstract = "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. ",

keywords = "Product of correlated normal random variables, probability density function, tail probability, quantile function, tail value at risk, asymptotic approximation",

author = "Robert Gaunt and Zixin Ye",

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AU - Gaunt, Robert

AU - Ye, Zixin

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N2 - 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.

AB - 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.

KW - Product of correlated normal random variables

KW - probability density function

KW - tail probability

KW - quantile function

KW - tail value at risk

KW - asymptotic approximation

UR - https://www.scopus.com/pages/publications/85208506709

U2 - 10.1016/j.jmaa.2024.128987

DO - 10.1016/j.jmaa.2024.128987

M3 - Article

SN - 0022-247X

VL - 543

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 128987

ER -

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

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Rates of Convergence in Multivariate Normal Approximation by Stein's Method

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Rates of Convergence in Multivariate Normal Approximation by Stein's Method

Cite this