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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Passau

Year

2020

Author dc:creator

• Hatzesberger, Simon

Contributors dc:contributor

• Müller-Gronbach, Thomas
• Sabanis, Sotirios

• Stochastic differential equation
• Strong approximation
• Strong asymptotic optimality
• Asymptotic lower error bounds
• Asymptotic upper error bounds

Statement dc:rights

• Creative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International

Repository record source_url

https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/810

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-passau:810