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Theory of Probability and Mathematical Statistics

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A semi-martingale representation for a semi-Markov chain with application to finance


Authors: R. Elliott, A. Swishchuk and I. Y. Zhang
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 96 (2017).
Journal: Theor. Probability and Math. Statist. 96 (2018), 45-57
MSC (2010): Primary 60K15, 60K10, 60G42, 60G51, 91B28
DOI: https://doi.org/10.1090/tpms/1033
Published electronically: October 5, 2018
MathSciNet review: 3666871
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Abstract: In this paper we present the semi-martingale representation for a discrete time semi-Markov chain, and consider its application to a semi-Markov regime-switching binomial model in finance. We also introduce a semi-Markov switching Lévy process. Estimation results for Markov and semi-Markov chains are presented as well.


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Additional Information

R. Elliott
Affiliation: University of Calgary, Calgary, Canada and University of South Australia
Email: relliott@ucalgary.ca

A. Swishchuk
Affiliation: University of Calgary, Calgary, Canada
Email: aswish@ucalgary.ca

I. Y. Zhang
Affiliation: University of Calgary, Calgary, Canada
Email: yi.zhang@ucalgary.ca

DOI: https://doi.org/10.1090/tpms/1033
Keywords: Discrete time finite state semi-Markov chain, semi-Markov switching L\'evy process, semi-martingale representation, financial derivatives, regime-switching binomial model
Received by editor(s): February 27, 2017
Published electronically: October 5, 2018
Dedicated: Dedicated to the 70th Anniversary of Professor Dmitrii Silvestrov
Article copyright: © Copyright 2018 American Mathematical Society