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Sampling error of the supremum of a Lévy process
Chen, Ao
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https://hdl.handle.net/2142/26321
Description
- Title
- Sampling error of the supremum of a Lévy process
- Author(s)
- Chen, Ao
- Issue Date
- 2011-08-26T15:22:53Z
- 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
- Date of Ingest
- 2011-08-26T15:22:53Z
- 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.
- Graduation Semester
- 2011-08
- Permalink
- http://hdl.handle.net/2142/26321
- Copyright and License Information
- Copyright 2011 Ao Chen
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