Kolmogorov equations arising in finance: direct and inverse problems

Kolmogorov Equations in Physics and in Finance

This paper contains a survey of results about linear and nonlinear partial differential equations of Kolmogorov type arising in physics and in mathematical finance. Some recent pointwise estimates proved in collaboration with S. Polidoro are also presented. Mathematics Subject Classification (2000). AMS Subject Classification: 35K57, 35K65, 35K70.

On Kolmogorov equations for anisotropic multivariate Lévy processes

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 aniso...

Special Solutions to Some Kolmogorov Equations Arising from Cubic Sensor Problems

Non-isothermal Crystallization of Polymers

This paper is devoted to the study of mathematical problems arising in the modelling of nonisothermal polymer crystallization under industrial conditions. A review of the hybrid stochastic-deterministic modelling procedure, which yields an averaged model 5;8 , is given and supplied by the study of mathematical problems arising from it. Furthermore, multiple scale eeects in the crystallization p...

Degenerate Diffusion Operators Arising in Population Biology

We analyze a class of partial differential equations that arise as"backwards Kolmogorov operators"in infinite population limits of the Wright-Fisher models in population genetics and in mathematical finance. These are degenerate elliptic operators defined on manifolds with corners. The classical example is the Kimura diffusion operator, which acts on functions defined on the simplex in R^n. We ...