Hullmann, Alexander: The ANOVA decomposition and generalized sparse grid methods for the high-dimensional backward Kolmogorov equation. - Bonn, 2015. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-39076
@phdthesis{handle:20.500.11811/6414,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-39076,
author = {{Alexander Hullmann}},
title = {The ANOVA decomposition and generalized sparse grid methods for the high-dimensional backward Kolmogorov equation},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2015,
month = mar,

note = {In this thesis, we discuss numerical methods for the solution of the high-dimensional backward Kolmogorov equation, which arises in the pricing of options on multi-dimensional jump-diffusion processes.
First, we apply the ANOVA decomposition and approximate the high-dimensional problem by a sum of lower-dimensional ones, which we then discretize by a θ-scheme and generalized sparse grids in time and space, respectively. We solve the resultant systems of linear equations by iterative methods, which requires both preconditioning and fast matrix-vector multiplication algorithms. We make use of a Linear Program and an algebraic formula to compute optimal diagonal scaling parameters. Furthermore, we employ the OptiCom as non-linear preconditioner. We generalize the unidirectional principle to non-local operators and develop a new matrix-vector multiplication algorithm for the OptiCom.
As application we focus on the Kou model. Using a new recurrence formula, the computational complexity of the operator application remains linear in the number of degrees of freedom. The combination of the above-mentioned methods allows us to efficiently approximate the solution of the backward Kolmogorov equation for a ten-dimensional Kou model.},

url = {http://hdl.handle.net/20.500.11811/6414}
}

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