A splitting method for fully nonlinear degenerate parabolic PDEs

A splitting method for fully nonlinear degenerate parabolic PDEs

Motivated by applications in Asian option pricing, optimal commodity trading etc., we propose a splitting scheme for fully nonlinear degenerate parabolic PDEs. The splitting scheme generalizes the probabilistic scheme of Fahim, Touzi and Warin [13] to the degenerate case. General convergence as well as rate of convergence are obtained under reasonable conditions. In particular, it can be used f...

A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs

We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in [10], and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-time approximation and derives a bound on the discretizat...

Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs

We prove a comparison result for viscosity solutions of (possibly degenerate) parabolic fully nonlinear path-dependent PDEs. In contrast with the previous result in Ekren, Touzi & Zhang [10], our conditions are easier to check and allow for the degenerate case, thus including first order path-dependent PDEs. Our argument follows the regularization method as introduced by Jensen, Lions & Sougani...

Homogenization of periodic semilinear parabolic degenerate PDEs

In this paper a second order semilinear parabolic PDE with rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some part of Rd . Our fully probabilistic method is based on the deep connection between PDEs and BSDEs and the weak convergence of a class of diffusion processe...

Infinite dimensional backstepping for nonlinear parabolic PDEs