## Journal of Applied Mathematics

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

### The Sum and Difference of Two Lognormal Random Variables

#### 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