Theory of Probability and Mathematical Statistics
A SEMI-MARTINGALE REPRESENTATION FOR A SEMI-MARKOV CHAIN WITH APPLICATION TO FINANCE
R. ELLIOTT, A. SWISHCHUK, I. Y. ZHANG
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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 nance. We also introduce a semi-Markov switching Levy process. Estimation results for a Markov and semi-Markov chains are presented as well.
Keywords: Discrete time nite state semi-Markov chain, semi-Markov switching Levy process, semi-martingale representation, nancial derivatives, regime-switching binomial model.
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