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Some Fluctuation Identities of Hyper-Exponential Jump-Diffusion Processes

Title:

Some Fluctuation Identities of Hyper-Exponential Jump-Diffusion Processes

Vu, Nhat Linh (2016) Some Fluctuation Identities of Hyper-Exponential Jump-Diffusion Processes. Masters thesis, Concordia University.

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Abstract

Meromorphic L´evy 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 L´evy 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.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Vu, Nhat Linh
Institution:Concordia University
Degree Name:M.Sc.
Program:Mathematics
Date:29 August 2016
Thesis Supervisor(s):Zhou, Xiaowen
ID Code:981562
Deposited By: NHAT LINH VU
Deposited On:08 Nov 2016 19:50
Last Modified:18 Jan 2018 17:53
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