Zhang, Xin; Elliott, Robert J.; Siu, Tak Kuen; Guo, Junyi Markovian regime-switching market completion using additional Markov jump assets. (English) Zbl 1280.91078 IMA J. Manag. Math. 23, No. 3, 283-305 (2012). Summary: 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. Cited in 4 Documents MSC: 91B25 Asset pricing models (MSC2010) 60H30 Applications of stochastic analysis (to PDEs, etc.) 60J27 Continuous-time Markov processes on discrete state spaces 91G20 Derivative securities (option pricing, hedging, etc.) Keywords:Markovian regime-switching markets; double martingales; martingale representation; market completion; marked point processes PDFBibTeX XMLCite \textit{X. Zhang} et al., IMA J. Manag. Math. 23, No. 3, 283--305 (2012; Zbl 1280.91078) Full Text: DOI