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Convex minorants and the simulation of the extrema of Lévy processes
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González Cázares, Jorge Ignacio (2021) Convex minorants and the simulation of the extrema of Lévy processes. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3765586
Abstract
In this thesis we will establish the stick-breaking representation of the convex minorant and the extrema of an arbitrary Levy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex functions and requires only very basic properties of Levy processes. We then use the stick-breaking representation to create geometrically convergent simulation algorithm for the extrema of a Levy process whose increments can be sampled. For processes whose increments cannot be sampled we develop a multilevel Monte Carlo algorithm using the stick-breaking representation. In all cases, the algorithms present in this thesis outperform the existing algorithms in the literature.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Lévy processes, Convex functions, Perfect simulation (Statistics), Algorithms | ||||
Official Date: | December 2021 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Mijatović, Aleksandar | ||||
Sponsors: | Consejo nacional de ciencia y tecnología (México) ; Alan Turing Institute | ||||
Format of File: | |||||
Extent: | iv, 130 leaves : illustrations | ||||
Language: | eng |
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