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