Lubin Georgiev Vulkov (Ruse State University): Adequate numerical methods for nonlinear parabolic problems in mathematical finance

The prices and hedjing strategies in the real financial  market models are often described by fully  nonlinear versions of the standard Black-Sholes equation. We concentrate on two classes of models: first, nonlinear Black-Sholes equations in which the volatility depends on  second space derivatives of the price(=solution) and then on regime-switching models described by systems of semilinear parabolic equations with exponential nonlinearities. The following characteristic  properties of these parabolic problems are typical: unbounded domain, boundary degeneration, maximum-minimum principle and nonnegativity preservation. We develop effective discretizations that reproduce these properties.