Σεμινάριο Υπολογιστικών Μαθηματικών

Πέμπτη 11 Ιανουαρίου 2018 (A303: 12.15-13.00)

Christina Christara
Department of Computer Science,
University of Toronto

Τitle: PDE option pricing with stochastic correlations

Abstract: Correlation between financial quantities plays an important role in pricing financial derivatives. Existing popular models assume that correlation either is constant, or exhibits some deterministic behaviour. However, market observations suggest that correlation is a more complicated process. We consider correlation structures guided by a stochastic mean-reverting process. We derive the related Partial Differential Equation (PDE) problems for pricing several types of financial derivatives, and solve them by accurate and efficient numerical methods. We study various numerical issues arising. We also consider correlation structures guided by regime switching, and derive and solve the associated PDE problems. We also study the effect of model parameters to the prices. We compare the results from the two types of correlation structures to each other and to results from Monte-Carlo simulations.

Joint work with Nat H.C. Leung

Παρασκευή 29 Σεπτεμβρίου 2017 (A303: 10.15-11.00)

Ιωάννης Τουλόπουλος
Johann Radon Institute for Computational and Applied Mathematics (RICAM),
Austrian Academy of Sciences

Τitle: Space-Time methods for parabolic evolution problems

Abstract: In this talk, we will present a space-time finite element method, and a new timemultipatch discontinuous Galerkin Isogeometric Analysis technology for solving parabolic initial-boundary problems. We prove coercivity of the discrete problems with respect to a suitably chosen norm that together with boundedness, consistency and approximation results yields a priori discretization error estimates in this norm. Furthermore, we will discuss efficient parallel multigrid solution technologies for solving the resulting algaibraic system. At the end, numerical examples will be shown that confirm the theoretical results. This talk is based on the works [1] and [2]. We gratefully acknowledge the financial support of this research work by the Austrian Science Fund (FWF) under the grant NFN S117-03.

References
[1] I. Toulopoulos. Stabilized space-time finite element methods of parabolic evolution problems. RICAM Report No. 2017-19 .
[2] C. Hofer, U. Langer, M. Neumüller and I. Toulopoulos. Time Discontinuous Galerkin Space-Time Isogeometric Analysis of Parabolic Problems. RICAM Report No. 2017-26 .

Τετάρτη 21 Ιουνίου 2017 (A303: 11.15-12.00)

Βικτωρία Ταρουδάκη
Eastern Washington University

Τitle: Images and sounds: How to remove blur and noise from received signals

Abstract: Signals that are transmitted and received from various devices (hydrophones, MRI scanners, digital cameras) are in general contaminated by blur and noise. For all the applications that are associated with everyday life and research, from just image watching to an elaborate exploitation of the signal in inverse problems of imaging or acoustics, it is crucial that the signals are as clear as possible so that the information they contain is retrievable with reliability. In this talk we will show a statistical near-optimal method to remove blur and noise from both one dimensional (acoustic) and two dimensional signals (images). In particular, we will show examples of how the method can be applied to MRI images, everyday images (e.g. photos) and acoustical signals giving satisfactory results for the associated applications.