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
Date Written: January 2013
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: Suggested Citation