A priori error estimates for reduced order models in finance

Ekkehard W. Sachs; Matthias Schu

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 2, page 449-469
  • ISSN: 0764-583X

Abstract

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

How to cite

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Sachs, Ekkehard W., and Schu, Matthias. "A priori error estimates for reduced order models in finance." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.2 (2013): 449-469. <http://eudml.org/doc/273315>.

@article{Sachs2013,
abstract = {Mathematical models for option pricing often result in partial differential equations. Recent enhancements are models driven by Lévy processes, which lead to a partial differential equation with an additional integral term. In the context of model calibration, these partial integro differential equations need to be solved quite frequently. To reduce the computational cost the implementation of a reduced order model has shown to be very successful numerically. In this paper we give a priori error estimates for the use of the proper orthogonal decomposition technique in the context of option pricing models.},
author = {Sachs, Ekkehard W., Schu, Matthias},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {option pricing models; proper orthogonal decomposition; a priori error estimate; error estimates; integro-partial differential equations; reduced-order model},
language = {eng},
number = {2},
pages = {449-469},
publisher = {EDP-Sciences},
title = {A priori error estimates for reduced order models in finance},
url = {http://eudml.org/doc/273315},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Sachs, Ekkehard W.
AU - Schu, Matthias
TI - A priori error estimates for reduced order models in finance
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 2
SP - 449
EP - 469
AB - Mathematical models for option pricing often result in partial differential equations. Recent enhancements are models driven by Lévy processes, which lead to a partial differential equation with an additional integral term. In the context of model calibration, these partial integro differential equations need to be solved quite frequently. To reduce the computational cost the implementation of a reduced order model has shown to be very successful numerically. In this paper we give a priori error estimates for the use of the proper orthogonal decomposition technique in the context of option pricing models.
LA - eng
KW - option pricing models; proper orthogonal decomposition; a priori error estimate; error estimates; integro-partial differential equations; reduced-order model
UR - http://eudml.org/doc/273315
ER -

References

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