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Sampling error of the supremum of a Lévy process

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Title: Sampling error of the supremum of a Lévy process
Author(s): Chen, Ao
Director of Research: Song, Renming; Feng, Liming
Doctoral Committee Chair(s): Bauer, Robert
Doctoral Committee Member(s): Song, Renming; Feng, Liming; Sowers, Richard
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Levy process supremum discrete sampling sampling error
Abstract: This thesis is to study the expected difference of the continuous supremum and discrete maximum of a Lévy process that is often used in finance. We will show that the expected difference is a quantity that highly depends on the variational property of the underlying Lévy process. Two techniques are used with respect to the cases of the complexity of the transition density function of the underlying Lévy process. In particular, we discuss the cases of Merton's jump diffusion, compound Poisson with normal jumps, normal inverse Gaussian process, variance gamma process, Kou's jump diffusion and (symmetric) stable process. A general result on the upper bound estimate for the expected difference is also shown.
Issue Date: 2011-08-26
Rights Information: Copyright 2011 Ao Chen
Date Available in IDEALS: 2013-08-27
Date Deposited: 2011-08

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