Inria / Raweb 2004
Team: Mathfi

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Team : mathfi

Section: New Results


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

Numerical methods for PDEs in Finance

Participants: Y. Achdou (Prof. Paris 6 University), D. Pommier, J. Printems, A. Zanette.

Sparse grids methods for PDEs in Mathematical Finance

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

Sparse grids methods are special variants of the Finite Element Method and are useful when the dimension (e.g. number of assets) increases. It relies on the approximation of functions defined on a domain of Rd by means of special tensor products of 1-d finite elements. These special products are those for which the indices are in the unit simplex. These methods are known to be efficient when the solutions are enough regular (see [56][94][92]). Our work consists in generalize the ideas of ``sparse grids'' to the regions where we can not control the regularity of the solution (typically near the maturity in Finance).

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

Adaptive finite element discretizations

Participants: A. Zanette, A. Ern (ENPC), S. Villeneuve (Toulouse university):

We perform numerical studies on adaptive finite element discretizations for pricing and hedging European options with local volatility Black-Scholes models. [20]

Lattice based methods for American options

Participants: A. Zanette (in collaboration with M.Gaudenzi, F.Pressacco and L.Ziani):

With reference to the evaluation of the speed/precision efficiency of pricing and hedging of American Put options, we present and discuss numerical results in [29][28]. A comparison of the best lattice based numerical methods known in literature is offered along with some key methodological remarks.


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