The sum and difference of two lognormal random variables
type: Item
instance of: scholarly article
title: The sum and difference of two lognormal random variables
zbMATH Open document ID: 1260.60018
DOI: 10.1155/2012/838397
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: We present a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum of \(N\) lognormals and (2) the sum and difference of other correlated stochastic processes, for example, two correlated constant-elasticity-of-variance processes, two correlated CIR processes, or two correlated lognormal processes with mean-reversion.
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 6106325
zbMATH Keywords: sum and difference
zbMATH Keywords: correlated lognormal stochastic variables
zbMATH Keywords: Lie-Trotter operator splitting method
zbMATH Keywords: analytical series expansion
Wikidata QID: Q58907442
author: Chi-Fai Lo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/838397
OpenAlex ID: W3122002512
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DBLP publication ID: journals/jam/Lo12
description: scientific article; zbMATH DE number 6106325