Quasi-Monte Carlo-Methods: From pure Number-Theory to Mathematical Finance

Friday 6 Nov 2015, 09:00 → 10:00 Europe/Zurich

30/7-010 (CERN)

Gerhard LARCHER (Institute for Financial Mathematics and Applied Number Theory, Johannes Kepler University Linz)

In this talk first we present the Austrian special research area (SFB) "Quasi-Monte Carlo-Methods: Theory and Applications" of the Austrian Science Fund (FWF), which is situated at the Johannes Kepler University Linz. Then we give an introduction to the basic principles of quasi-Monte Carlo-Methods and to relevant research topics in the theory and in the applications of Quasi-Monte Carlo methods. Especially we will point out that the development of efficient quasi-Monte Carlo methods (a in a certain sense deterministic version of classical plain Monte Carlo simulation methods) often leads to hard open problems in pure mathematics, especially in number theory. We will give some examples of such challenging open theoretical problems. Concerning applications we essentially will be focused on examples from mathematical finance. Finally we will point out a very recent development, so-called hybrid Monte Carlo-methods. Here plain Monte Carlo methods and quasi-Monte Carlo methods are combined in a suitable and efficient way.

Präsentation_Larcher_CERN.pdf