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hp-DGFEM for Kolmogorov-Fokker-Planck equations of multivariate Levy processes
(2011)Presentation -
DG-FEM for Option Pricing in Levy Models
(2011)We analyze the discretization of non-local degenerate integrodifferential equations arising as so-called forward equations for jump-diffusion processes, in particular in option pricing problems when dealing with Lévy driven stochastic volatility models. Well-posedness of the arising equations is addressed. We develop and analyse stable discretization schemes. A discontinuous Galerkin (DG) Finite Element Method is analyzed. In the DG-FEM, ...Presentation -
Space-Time Wavelet Methods for degenerate parabolic PDEs with applications to Fractional Brownian motion models
(2011)We analyze parabolic PDEs with certain type of weakly singular or degenerate time-dependent coefficients and prove existence and uniqueness of weak solutions in an appropriate sense. For the numerical solution a weak space-time formulation is considered, as a possible singularity or degeneracy of the diffusion coefficients impedes the application of classical parabolic theory. We analyze parabolic PDEs with certain type of weakly singular ...Presentation -
hp-DGFEM for Kolmogorov-Fokker-Planck Equations of Multivariate Lévy Processes
(2011)Presentation