Journal of Applied Mathematics

The Sum and Difference of Two Lognormal Random Variables

C. F. Lo

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 838397, 13 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495293

Digital Object Identifier
doi:10.1155/2012/838397

Mathematical Reviews number (MathSciNet)
MR2970432

Zentralblatt MATH identifier
1260.60018

Citation

Lo, C. F. The Sum and Difference of Two Lognormal Random Variables. J. Appl. Math. 2012 (2012), Article ID 838397, 13 pages. doi:10.1155/2012/838397. https://projecteuclid.org/euclid.jam/1355495293


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