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Type: Journal article
Title: Markovian regime-switching market completion using additional Markov jump assets
Author: Zhang, X.
Elliott, R.
Siu, T.
Guo, J.
Citation: IMA Journal of Management Mathematics, 2012; 23(3):283-305
Publisher: Oxford Unversity Press, Journals
Issue Date: 2012
ISSN: 1471-678X
Statement of
Xin Zhang, Robert J. Elliott, Tak Kuen Siu and Junyi Guo
Abstract: In this paper, we discuss the use of some representation results for double martingales to value and hedge contingent claims in a Markovian regime-switching market. A set of N Markov jump assets is introduced to complete the Markovian regime-switching market. Using a representation for double martingales, we justify the completeness of the enlarged market. An equivalent martingale measure, or price kernel, in the enlarged market is then identified by a measure change. The option pricing formula and the hedging portfolio in the enlarged market is also discussed.
Keywords: Markovian regime-switching markets
double martingales
martingale representation
market completion
marked point processes
Rights: © The authors 2011
DOI: 10.1093/imaman/dpr018
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