Integration by parts and martingale representation for a Markov Chain

Tak Kuen Siu

doi:10.1155/2014/438258

Integration by parts and martingale representation for a Markov Chain

Tak Kuen Siu^*

^*Corresponding author for this work

Department of Applied Finance

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

142 Downloads (Pure)

Abstract

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.

Original language	English
Article number	438258
Pages (from-to)	1-11
Number of pages	11
Journal	Abstract and Applied Analysis
Volume	2014
DOIs	https://doi.org/10.1155/2014/438258
Publication status	Published - 2014

Bibliographical note

Copyright the Author 2014. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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AB - 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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Integration by parts and martingale representation for a Markov Chain

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