{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/26321"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/26321","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Sampling error of the supremum of a Lévy process","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Chen, Ao"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Song, Renming","Feng, Liming","Bauer, Robert","Sowers, Richard B."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-08-26T15:22:53Z","date_published":"2011-08-26T15:22:53Z","updated_at":"2026-07-22T22:25:26Z","subjects":["Levy process","supremum","discrete sampling","sampling error"],"languages":["en"],"rights":["Copyright 2011 Ao Chen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/26321","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Song, Renming","Feng, Liming","Bauer, Robert","Sowers, Richard B."]},{"key":"dc:creator","label":"Author","values":["Chen, Ao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-08-26T15:22:53Z","2013-08-27T10:00:22Z","2011-08"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Levy process","supremum","discrete sampling","sampling error"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2011 Ao Chen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/26321"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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. 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