The Sum and Difference of Two Lognormal Random Variables
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 probab...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/838397 |
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| _version_ | 1841524708949884928 |
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| author | C. F. Lo |
| author_facet | C. F. Lo |
| author_sort | C. F. Lo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-17d0e3b78801448e94db312e129dd548 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-17d0e3b78801448e94db312e129dd5482025-02-03T05:47:31ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/838397838397The Sum and Difference of Two Lognormal Random VariablesC. F. Lo0Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Hong KongWe 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.http://dx.doi.org/10.1155/2012/838397 |
| spellingShingle | C. F. Lo The Sum and Difference of Two Lognormal Random Variables Journal of Applied Mathematics |
| title | The Sum and Difference of Two Lognormal Random Variables |
| title_full | The Sum and Difference of Two Lognormal Random Variables |
| title_fullStr | The Sum and Difference of Two Lognormal Random Variables |
| title_full_unstemmed | The Sum and Difference of Two Lognormal Random Variables |
| title_short | The Sum and Difference of Two Lognormal Random Variables |
| title_sort | sum and difference of two lognormal random variables |
| url | http://dx.doi.org/10.1155/2012/838397 |
| work_keys_str_mv | AT cflo thesumanddifferenceoftwolognormalrandomvariables AT cflo sumanddifferenceoftwolognormalrandomvariables |