  We propose an approximation scheme for a class of semilinear parabolic
equations that are convex and coercive in their gradients. Such equations arise
often in pricing and portfolio management in incomplete markets and, more
broadly, are directly connected to the representation of solutions to backward
stochastic differential equations. The proposed scheme is based on splitting
the equation in two parts, the first corresponding to a linear parabolic
equation and the second to a Hamilton-Jacobi equation. The solutions of these
two equations are approximated using, respectively, the Feynman-Kac and the
Hopf-Lax formulae. We establish the convergence of the scheme and determine the
convergence rate, combining Krylov's shaking coefficients technique and
Barles-Jakobsen's optimal switching approximation.
