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

نویسنده

  • Christoph Reisinger
چکیده

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 [GG03], anchored ANOVA decompositions and dimension-wise integration [GH10], and the embedding in infinite-dimensional weighted spaces [SW98]. 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.

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تاریخ انتشار 2011