A splitting method for fully nonlinear degenerate parabolic PDEs

Xiaolu Tan (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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 stochas-tic control problems or stochastic differential games. We also provide a simulation-regression 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.

Mots clés: Numerical scheme; nonlinear degenerate PDE; splitting method; viscosity solu-tion AMS MSC 2010: Primary 65C05; secondary 49L25

Domaines: Probabilités [math.PR]

Xiaolu Tan. A splitting method for fully nonlinear degenerate parabolic PDEs. Electronic Journal of Probability, 2013, ⟨10.1214/EJP.v18-1967⟩. ⟨hal-01246999⟩