Sampling error of the supremum of a Lévy process

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Chen, Ao

Contributors dc:contributor

• Song, Renming
• Feng, Liming
• Bauer, Robert
• Sowers, Richard B.

• Levy process
• supremum
• discrete sampling
• sampling error

Statement dc:rights

• Copyright 2011 Ao Chen

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/26321

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/26321