Integration by Parts and Martingale Representation for a Markov Chain
Integration-by-parts formulas for functions of fundamental jump processes relating to a continuous-time, finite-state Markov chain are derived using Bismut's change of measures approach to Malliavin calculus. New expressions for the integrands in stochastic integrals corresponding to representa...
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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/10.1155/2014/438258 |
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| _version_ | 1832555515873329152 |
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| author | Tak Kuen Siu |
| author_facet | Tak Kuen Siu |
| author_sort | Tak Kuen Siu |
| collection | DOAJ |
| description | Integration-by-parts formulas for functions of fundamental jump processes relating to a continuous-time, finite-state Markov chain are derived using Bismut's change of measures approach to Malliavin calculus. New expressions for the integrands in stochastic integrals corresponding to representations of martingales for the fundamental jump processes are derived using the integration-by-parts formulas. These results are then applied to hedge contingent claims in a Markov chain financial market, which provides a practical motivation for the developments of the integration-by-parts formulas and the martingale representations. |
| format | Article |
| id | doaj-art-21412f6d1a454d129001581b11bb4d4f |
| 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-21412f6d1a454d129001581b11bb4d4f2025-02-03T05:47:58ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/438258438258Integration by Parts and Martingale Representation for a Markov ChainTak Kuen Siu0Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, UKIntegration-by-parts formulas for functions of fundamental jump processes relating to a continuous-time, finite-state Markov chain are derived using Bismut's change of measures approach to Malliavin calculus. New expressions for the integrands in stochastic integrals corresponding to representations of martingales for the fundamental jump processes are derived using the integration-by-parts formulas. These results are then applied to hedge contingent claims in a Markov chain financial market, which provides a practical motivation for the developments of the integration-by-parts formulas and the martingale representations.http://dx.doi.org/10.1155/2014/438258 |
| spellingShingle | Tak Kuen Siu Integration by Parts and Martingale Representation for a Markov Chain Abstract and Applied Analysis |
| title | Integration by Parts and Martingale Representation for a Markov Chain |
| title_full | Integration by Parts and Martingale Representation for a Markov Chain |
| title_fullStr | Integration by Parts and Martingale Representation for a Markov Chain |
| title_full_unstemmed | Integration by Parts and Martingale Representation for a Markov Chain |
| title_short | Integration by Parts and Martingale Representation for a Markov Chain |
| title_sort | integration by parts and martingale representation for a markov chain |
| url | http://dx.doi.org/10.1155/2014/438258 |
| work_keys_str_mv | AT takkuensiu integrationbypartsandmartingalerepresentationforamarkovchain |