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Section: New Results

Keywords : sparse grids, finite element, adaptive finite elements, lattice-based methods.

Sparse grids methods for PDEs in Mathematical Finance

Participants : Y. Achdou, D. Pommier, J. Printems.

In some applications in finance for example the pricing of option on baskets of dassets, the efficient numerical solutions to elliptic partial differential equations (PDEs) in high dimension is necessary. The application of standard numerical schemes fails due to the 'curse of dimension' which means the exponential dependence on the dimension of the number of degrees of freedom. To cope with the 'curse of dimension', so called sparse grids have been proposed by Zenger [109] (see [71] ). The sparse grids approach is based on a d-dimensional tensor product basis, which is derived from a one-dimensional hierarchical basis. We use a Galerkin method with wavelets as hierarchical basis (see [108] ). Our work consists in reducing time computing by adapting the wavelet basis to sparse tensor product.

A Cifre agreement on this subject between Inria and CIC is engaged involving the PhD student David Pommier.


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