Director of Research (if dissertation) or Advisor (if thesis)
Song, Renming
Feng, Liming
Doctoral Committee Chair(s)
Bauer, Robert
Committee Member(s)
Song, Renming
Feng, Liming
Sowers, Richard B.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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