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Asymptotic Expansion Around Principal Components and the Complexity of Dimension Adaptive Algorithms

  • Christoph Reisinger
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 88)

Abstract

In this short article, we describe how the correlation of typical diffusion processes arising e.g. in financial modelling can be exploited—by means of asymptotic analysis of principal components—to make Feynman-Kac PDEs of high dimension computationally tractable. We explore the links to dimension adaptive sparse grids (Gerstner and Griebel, Computing 71:65–87, 2003), anchored ANOVA decompositions and dimension-wise integration (Griebel and Holtz, J Complexity 26:455–489, 2010), and the embedding in infinite-dimensional weighted spaces (Sloan and Woźniakowski, J Complexity 14:1–33, 1998). The approach is shown to give sufficient accuracy for the valuation of index options in practice. These numerical findings are backed up by a complexity analysis that explains the independence of the computational effort of the dimension in relevant parameter regimes.

Keywords

Sparse Grid Finite Element Scheme Basket Option Central Finite Difference Scheme Superposition Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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