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A priori error estimates for reduced ordermodels in finance∗

Published online by Cambridge University Press:  11 January 2013

Ekkehard W. Sachs  and
Matthias Schu
Ekkehard W. Sachs
Affiliation:
Universität Trier, Fachbereich IV, Abteilung Mathematik, 54286 Trier, Germany.. sachs@uni-trier.de; schu@uni-trier.de
Matthias Schu
Affiliation:
Universität Trier, Fachbereich IV, Abteilung Mathematik, 54286 Trier, Germany.. sachs@uni-trier.de; schu@uni-trier.de
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Abstract

Mathematical models for option pricing often result in partial differential equations.Recent enhancements are models driven by Lévy processes, which lead to a partialdifferential equation with an additional integral term. In the context of modelcalibration, these partial integro differential equations need to be solved quitefrequently. To reduce the computational cost the implementation of a reduced order modelhas shown to be very successful numerically. In this paper we give a priorierror estimates for the use of the proper orthogonal decomposition technique inthe context of option pricing models.

Keywords

Option pricing modelsproper orthogonal decompositiona priori error estimate
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 2 , March 2013 , pp. 449 - 469
Copyright
© EDP Sciences, SMAI, 2013

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