Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model

In this thesis, we consider the use of the sparse grid combination technique with finite difference methods to solve parabolic partial differential equations. Convergence results are obtained in L2 for arbitrary dimensions via Fourier analysis arguments under the assumption that the initial data lies in the Sobolev space H4 mix. Numerical results are presented for model problems and for problems from the field of option pricing.