Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance
We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/709871 |
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| _version_ | 1832552827097972736 |
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| author | Tanki Motsepa Chaudry Masood Khalique Motlatsi Molati |
| author_facet | Tanki Motsepa Chaudry Masood Khalique Motlatsi Molati |
| author_sort | Tanki Motsepa |
| collection | DOAJ |
| description | We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases. |
| format | Article |
| id | doaj-art-1d879ea8b7e64b05b0ff2408913b840a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1d879ea8b7e64b05b0ff2408913b840a2025-02-03T05:57:39ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/709871709871Group Classification of a General Bond-Option Pricing Equation of Mathematical FinanceTanki Motsepa0Chaudry Masood Khalique1Motlatsi Molati2International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaInternational Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaInternational Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaWe carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.http://dx.doi.org/10.1155/2014/709871 |
| spellingShingle | Tanki Motsepa Chaudry Masood Khalique Motlatsi Molati Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance Abstract and Applied Analysis |
| title | Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance |
| title_full | Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance |
| title_fullStr | Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance |
| title_full_unstemmed | Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance |
| title_short | Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance |
| title_sort | group classification of a general bond option pricing equation of mathematical finance |
| url | http://dx.doi.org/10.1155/2014/709871 |
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