Feynman–Kac formulas for regime-switching jump diffusions and their applications Article Swipe

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Chao Zhu , George Yin , Nicholas A. Baran ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.1080/17442508.2015.1019884 · OA: W1960719493

This work develops Feynman-Kac formulas for a class of regime-switching jump diffusion processes, in which the jump part is driven by a Poisson random measure associated to a general L\'evy process and the switching part depends on the jump diffusion processes. Under broad conditions, the connections of such stochastic processes and the corresponding partial integro-differential equations are established. Related initial, terminal, and boundary value problems are also treated. Moreover, based on weak convergence of probability measures, it is demonstrated that a sequence of random variables related to the regime-switching jump diffusion process converges in distribution to the arcsine law.