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Date
2008Type
- Report
ETH Bibliography
yes
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Abstract
For d-dimensional exponential L´evy models, variational formulations of the Kolmogorov equations arising in asset pricing are derived. Well-posedness of these equations is verified. Particular attention is paid to pure jump, d-variate L´evy processes built from parametric, copula dependence models in their jump structure. The domains of the associated Dirichlet forms are shown to be certain anisotropic Sobolev spaces. Representations of the Dirichlet forms are given which remain bounded for piecewise polynomial, continuous functions of finite element type. We prove that the variational problem can be localized to a bounded domain with explicit localization error bounds. Furthermore, we collect several analytical tools for further numerical analysis. Show more
Publication status
publishedJournal / series
Research reportsVolume
(3)Publisher
Seminar für Angewandte Mathematik, ETHSubject
L´evy-copulas; L´evy processes; integrodifferential equations; pseudo differential operators; Dirichlet forms; option pricingOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
03217 - Künsch, Hans Rudolf
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ETH Bibliography
yes
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