Nonlinear desingularization in certain free-boundary problems

A Stochastic Approximation for Fully Nonlinear Free Boundary Parabolic Problems

When the option pricing problem is of several dimensions, for example, basket options, deterministic methods such as finite difference are almost intractable; because the complexity increases exponentially with the dimension and one almost inevitably needs to use Monte Carlo simulations. Moreover, many problems in finance, for example, pricing in incomplete markets and portfolio optimization, l...

A Stochastic Approximation for Fully Nonlinear Free Boundary Problems

We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.

Free Boundary Problems for Nonlinear Wave Systems: Interacting Shocks

On Free Boundary Problems

Free Boundary Problems

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...