Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model

Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model

In this thesis, we consider the use of the sparse grid combination technique with finite difference methods to solve parabolic partial differential equations. Convergence results are obtained in L2 for arbitrary dimensions via Fourier analysis arguments under the assumption that the initial data lie...

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Main Author: Hausauer, Justin
Format: Others
Published: Research Showcase @ CMU 2015
Online Access:http://repository.cmu.edu/dissertations/519
http://repository.cmu.edu/cgi/viewcontent.cgi?article=1519&context=dissertations
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spelling ndltd-cmu.edu-oai-repository.cmu.edu-dissertations-15192015-09-01T03:30:18Z Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model Hausauer, Justin In this thesis, we consider the use of the sparse grid combination technique with finite difference methods to solve parabolic partial differential equations. Convergence results are obtained in L2 for arbitrary dimensions via Fourier analysis arguments under the assumption that the initial data lies in the Sobolev space H4 mix. Numerical results are presented for model problems and for problems from the field of option pricing. 2015-05-01T07:00:00Z text application/pdf http://repository.cmu.edu/dissertations/519 http://repository.cmu.edu/cgi/viewcontent.cgi?article=1519&context=dissertations Dissertations Research Showcase @ CMU
collection NDLTD
format Others
sources NDLTD
description In this thesis, we consider the use of the sparse grid combination technique with finite difference methods to solve parabolic partial differential equations. Convergence results are obtained in L2 for arbitrary dimensions via Fourier analysis arguments under the assumption that the initial data lies in the Sobolev space H4 mix. Numerical results are presented for model problems and for problems from the field of option pricing.
author Hausauer, Justin
spellingShingle Hausauer, Justin
Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model
author_facet Hausauer, Justin
author_sort Hausauer, Justin
title Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model
title_short Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model
title_full Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model
title_fullStr Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model
title_full_unstemmed Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model
title_sort sparse grid combination techniques for solving high-dimensional parabolic equations with an application to the libor market model
publisher Research Showcase @ CMU
publishDate 2015
url http://repository.cmu.edu/dissertations/519
http://repository.cmu.edu/cgi/viewcontent.cgi?article=1519&context=dissertations
work_keys_str_mv AT hausauerjustin sparsegridcombinationtechniquesforsolvinghighdimensionalparabolicequationswithanapplicationtothelibormarketmodel
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