A Convergent Difference Scheme for a Class of Partial Integro-Differential Equations Modeling Pricing under Uncertainty.

In this paper we present a finite difference scheme to approximate viscosity solutions of a class of partial integro-differential equations describing pricing under model uncertainty. We establish that the approximations converge to the unique viscosity solution as the discretization parameter tends to zero, and give an asymptotic rate of the convergence. We also present several numerical examples showing this convergence.