Dimension-Wise Decompositions and Their Efficient Parallelization

Electronic version of an article published in Recent Developments in Computational Finance, Interdisciplinary Mathematical Sciences, Volume 14, 2013, chapter 13, pages 445-472, DOI: 0.1142/9789814436434 0013(c) World Scientific Publishing Company

30 Pages Posted: 19 Apr 2015

See all articles by Philipp Schröder

Philipp Schröder

Goethe Center for Scientific Computing

Peter Schober

Goethe University Frankfurt - Department of Finance

Gabriel Wittum

Goethe Center for Scientific Computing

Date Written: January 2013

Abstract

Many problem classes in finance lead to high dimensional partial differential equations which need to be solved efficiently. To circumnavigate the curse of dimension several methods exist, e.g. dimension-wise decomposition techniques. In this chapter we will present an overview over the different methods available to cope with high dimensional problems. The class of dimension-wise decomposition methods, which we will discuss in detail, decomposes a high dimensional problem into a set of low dimensional problems. Dependent on the dimension d of the total problem, and the order of the decomposition method the number of low-dimensional problems can be quite large. This makes efficient parallelization techniques necessary.

Keywords: ANOVA Decomposition, High Performance Computing, Option Pricing, Partial Differential Equations, Parallelization, Sparse Grids

JEL Classification: C61, C63, G12, G13

Suggested Citation

Schröder, Philipp and Schober, Peter and Wittum, Gabriel, Dimension-Wise Decompositions and Their Efficient Parallelization (January 2013). Electronic version of an article published in Recent Developments in Computational Finance, Interdisciplinary Mathematical Sciences, Volume 14, 2013, chapter 13, pages 445-472, DOI: 0.1142/9789814436434 0013(c) World Scientific Publishing Company, Available at SSRN: https://ssrn.com/abstract=2595083

Philipp Schröder

Goethe Center for Scientific Computing ( email )

Grüneburgplatz 1
Frankfurt am Main, 60323
Germany

Peter Schober (Contact Author)

Goethe University Frankfurt - Department of Finance ( email )

House of Finance
Theodor-W.-Adorno Platz 3
Frankfurt am Main, Hessen 60323
Germany

Gabriel Wittum

Goethe Center for Scientific Computing ( email )

Grüneburgplatz 1
Frankfurt am Main, 60323
Germany

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