On Kolmogorov equations for anisotropic multivariate Lévy processes

@article{Reich2008OnKE,
  title={On Kolmogorov equations for anisotropic multivariate L{\'e}vy processes},
  author={Nils Reich and Christoph Schwab and Christoph Winter},
  journal={Finance and Stochastics},
  year={2008},
  volume={14},
  pages={527-567}
}
For d-dimensional exponential Lévy 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 Lévy 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. Singularity-free representations of the Dirichlet forms are given which remain… CONTINUE READING

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