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• W2561690588 abstract "IIn this paper we provide predictable and chaotic representations for Ito-Markov additive processes $X$. Such a process is governed by a finite-state CTMC $J$ which allows one to modify the parameters of the Ito-jump process (in so-called regime switching manner). In addition, the transition of $J$ triggers the jump of $X$ distributed depending on the states of $J$ just prior to the transition. This family of processes includes Markov modulated Ito-Levy processes and Markov additive processes. The derived chaotic representation of a square-integrable random variable is given as a sum of stochastic integrals with respect to some explicitly constructed orthogonal martingales. We identify the predictable representation of a square-integrable martingale as a sum of stochastic integrals of predictable processes with respect to Brownian motion and power-jumps martingales related to all the jumps appearing in the model. This result generalizes the seminal result of Jacod-Yor and is of importance in financial mathematics. The derived representation then allows one to enlarge the incomplete market by a series of power-jump assets and to price all market-derivatives." @default.
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• W2561690588 date "2016-12-29" @default.
• W2561690588 modified "2023-09-27" @default.
• W2561690588 title "A note on chaotic and predictable representations for It^o-Markov additive processes" @default.
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