A splitting method for fully nonlinear degenerate parabolic PDEs

Motivated by applications in Asian option pricing, optimal commodity trading etc., we propose a splitting scheme for fully nonlinear degenerate parabolic PDEs. The splitting scheme generalizes the probabilistic scheme of Fahim, Touzi and Warin [13] to the degenerate case. General convergence as well as rate of convergence are obtained under reasonable conditions. In particular, it can be used for a class of Hamilton-Jacobi-Bellman equations, which characterize the value functions of stochastic control problems or stochastic differential games. We also provide a simulationregression method to make the splitting scheme implementable. Finally, we give some numerical tests in an Asian option pricing problem and an optimal hydropower management problem.