Abstract
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, a new regularization of hypersingular integrals in the Dirichlet Form of the pure jump part of infinite variation processes is proposed. Robustness of the stabilized discretization with respect to various degeneracies in the characteristic triple of the stochastic process is proved. We provide in particular an hp-error analysis of the DG-FEM and numerical experiments. Show more
Publication status
unpublishedPublisher
Politecnico di Milano, Dipartimento di MatematicaEvent
Organisational unit
03435 - Schwab, Christoph / Schwab, Christoph
Notes
Invited Talk.More
Show all metadata
ETH Bibliography
yes
Altmetrics