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Strongly Asymptotically Optimal Methods for the Pathwise Global Approximation of Stochastic Differential Equations with Coefficients of Super-linear Growth

  • Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum and the L_p error criteria, and we seek approximations that are strongly asymptotically optimal in specific classes of approximations. For the supremum error, we prove strong asymptotic optimality for specific tamed Euler schemes relating to certain adaptive and to equidistant time discretizations. For the L_p error, we prove strong asymptotic optimality for specific tamed Milstein schemes relating to certain adaptive and to equidistant time discretizations. To illustrate our findings, we numerically analyze the SDE associated with the Heston–3/2–model originating from mathematical finance.

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Author:Simon HatzesbergerORCiD
URN:urn:nbn:de:bvb:739-opus4-8100
Advisor:Thomas Müller-Gronbach, Sotirios Sabanis
Document Type:Doctoral Thesis
Language:English
Year of Completion:2020
Date of Publication (online):2020/06/30
Date of first Publication:2020/06/30
Publishing Institution:Universität Passau
Granting Institution:Universität Passau, Fakultät für Informatik und Mathematik
Date of final exam:2020/02/21
Release Date:2020/06/30
Tag:Asymptotic lower error bounds; Asymptotic upper error bounds; Stochastic differential equation; Strong approximation; Strong asymptotic optimality
GND Keyword:Stochastische Differentialgleichung; Approximation
Page Number:ii, 116 Seiten
Institutes:Fakultät für Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
open_access (DINI-Set):open_access
Licence (German):License LogoCreative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International