  We extend the viscosity solution characterization proved in [5] for call/put
American option prices to the case of a general payoff function in a
multi-dimensional setting: the price satisfies a semilinear re-action/diffusion
type equation. Based on this, we propose two new numerical schemes inspired by
the branching processes based algorithm of [8]. Our numerical experiments show
that approximating the discontinu-ous driver of the associated
reaction/diffusion PDE by local polynomials is not efficient, while a simple
randomization procedure provides very good results.
