Non-homogeneous Markov and semi-Markov models for pricing derivative securities

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In this paper for the first time (as far as the authors know) an application of the non-homogeneous Markov and semi-Markov processes aimed at pricing derivative securities has been proposed. The consideration of the nonhomogeneity in the framework of the pricing derivative securities allows us to take into account also the possibility to differentiate the financial operations according to the starting time.