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Dimension-wise Quadrature

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Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 77))

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Abstract

High-dimensional integrals appear in various mathematical models from physics, chemistry or finance. The large number of dimensions arises, e.g., from small time steps in time discretizations and/or a large number of state variables. In many cases the arising integrals can not be calculated analytically and numerical methods must be applied. Here, one of the key prerequisites for a successful application is that the curse of dimension [7] can be avoided at least to some extent. The curse of dimension states that the cost to compute an approximation with a prescribed accuracy ε depends exponentially on the dimension d of the problem. It is one of the main obstacles for the numerical treatment of high dimensional problems, see, e.g., [57].

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  1. Universität Bonn, Institut für Numerische Simulation, Wegelerstr. 5, 53115, Bonn, Germany

    Markus Holtz

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  1. Markus Holtz
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Holtz, M. (2011). Dimension-wise Quadrature. In: Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance. Lecture Notes in Computational Science and Engineering, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16004-2_3

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