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The Sum and Difference of Two Lognormal Random Variables
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-10
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
We have presented 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 CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.
American Psychological Association (APA)
Lo, C. F.. 2012. The Sum and Difference of Two Lognormal Random Variables. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-993746
Modern Language Association (MLA)
Lo, C. F.. The Sum and Difference of Two Lognormal Random Variables. Journal of Applied Mathematics No. 2012 (2012), pp.1-13.
https://search.emarefa.net/detail/BIM-993746
American Medical Association (AMA)
Lo, C. F.. The Sum and Difference of Two Lognormal Random Variables. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-993746
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993746