We consider the valuation of derivative contracts on baskets of risky assets whose prices are Lévy like Feller processes of tempered stable type. The dependence among the marginals’ jump structure is parametrized by a Lévy copula. For marginals of regular, exponential Lévy type in the sense of [6] we show that the infinitesimal generator A of the resulting Lévy copula process is a pseudo-differential operator whose principal ...

We define the higher order moments associated to the stochastic solution of an elliptic BVP in D \subset Rd with stochastic source terms and boundary data. We prove that the k-th moment (or k-point correlation function) of the random solution solves a deterministic problem in Dk \subset Rdk. We discuss well-posedness and regularity in scales of Sobolev spaces with bounded mixed derivatives. We discretize this deterministic k-th moment ...

We establish multiresolution norm equivalences in weighted spaces $L^2_w$ ((0,1)) with possibly singular weight functions $w(x) \geq 0$ in (0,1). Our analysis exploits the locality of the biorthogonal wavelet basis and its dual basis functions. The discrete norms are sums of wavelet coefficients which are weighted with respect to the collocated weight function $w(x)$ within each scale. Since norm equivalences for Sobolev norms are by now ...

The algorithmic pattern of the hp Discontinuous Galerkin Finite Element Method (DGFEM) for the time semidiscretization of abstract parabolic evolution equations is presented. In combination with a continuous $hp$ discretization in space we present a fully discrete hp-scheme for the numerical solution of parabolic problems. Numerical examples for the heat equation in a two dimensional domain confirm the exponential convergence rates which ...