Monotone schemes for fully nonlinear parabolic path dependent PDEs

Abstract

In this paper, we extend the results of the seminal work Barles and Souganidis (1991) to path dependent case. Based on the viscosity theory of path dependent PDEs, developed by Ekren et al. (2012a, 2012b, 2014a and 2014b), we show that a monotone scheme converges to the unique viscosity solution of the (fully nonlinear) parabolic path dependent PDE. An example of such monotone scheme is proposed. Moreover, in the case that the solution is smooth enough, we obtain the rate of convergence of our scheme.