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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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 [via Doctoral College] (PhD) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Library of Congress Subject Headings (LCSH): | Lévy processes, Convex functions, Perfect simulation (Statistics), Algorithms |
| Official Date: | December 2021 |
| Dates: | Date Event December 2021 UNSPECIFIED |
| 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| Publication Status: | Unpublished |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 |
| URI: | https://wrap.warwick.ac.uk/166261/ |
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