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Abstract We prove a Feynman–Kac-type theorem for jump-diffusion models in random environments. We consider the Cauchy and Dirichlet problems. Our results enable us to calculate some conditional expectations using related… Click to show full abstract
Abstract We prove a Feynman–Kac-type theorem for jump-diffusion models in random environments. We consider the Cauchy and Dirichlet problems. Our results enable us to calculate some conditional expectations using related partial integro-differential equations (PIDEs) and vice versa to solve some PIDEs by stochastic methods. So, the results may have many applications. We illustrate the use of our results on an example of a generalized exponential Levy model with regime-switching.
Keywords:
integro differential;
random environments;
partial integro;
feynman kac;
differential equations;
kac theorem
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!