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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Main Author: Tak Kuen Siu
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/438258
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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.
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institution Kabale University
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language English
publishDate 2014-01-01
publisher Wiley
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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