Branching diffusion simulation for stochastic control problems with friction

Using branching processes, we give a numerical method for the simulation of solutions of systems of nonlinear PDEs where the nonlinearity is polynomial on the unknown functions. Under some integrability assumption we show the... [ view full abstract ]

Using branching processes, we give a numerical method for the simulation of solutions of systems of nonlinear PDEs where the nonlinearity is polynomial on the unknown functions. Under some integrability assumption we show the convergence of the method. Using a transformation, we apply these methods for the simulation of solutions of a class of degenerate parabolic PDEs coming from stochastic control problems with frictions. In this case, we also exhibit assumptions proving the convergence of the method.