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Some Fluctuation Identities of Hyper-Exponential Jump-Diffusion Processes

Nhat Linh Vu

出版	Concordia University, 2016
URL	http://books.google.com.hk/books?id=T-pUyQEACAAJ&hl=&source=gbs_api

註釋

Meromorphic Ĺevy processes have attracted the attention of a lot of researchers recently due to its special structure of the Wiener-Hopf factors as rational functions of infinite degree written in terms of poles and roots of the Laplace exponent, all of which are real numbers. With these Wiener-Hopf factors in hand, we can explicitly derive the expression of fluctuation identities that concern the first passage problems for finite and infinite intervals for the meromorphic Ĺevy process and the resulting process reflected at its infimum. In this thesis, we consider some fluctuation identities of some classes of meromorphic jump-diffusion processes with either the double exponential jumps or more general the hyper-exponential jumps. We study solutions to the one-sided and two-sided exit problems, and potential measure of the process killed on exiting a finite or infinite intervals. Also, we obtain some results to the process reflected at its infimum.