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 schemeâ€¦ (More)

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.

This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. It hasâ€¦ (More)

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 increasesâ€¦ (More)

Consider a discrete uniformly elliptic divergence form equation on the d â‰¥ 3 dimensional lattice Zd with random coefficients. In [3] rate of convergence results in homogenization and estimates on theâ€¦ (More)

In this paper, we introduce a probabilistic numerical scheme for a class of parabolic and elliptic fully non-linear PDEs in bounded domains. In the main result, we provide the convergence of aâ€¦ (More)

We introduce a Monte Carlo scheme for the approximation of the solutions of fully nonâ€“linear parabolic nonâ€“local PDEs. The method is the generalization of the method proposed by [Fahim-Touzi-Warin,â€¦ (More)

This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. In [11]â€¦ (More)

This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider optimalâ€¦ (More)