Accurate Semi-Lagrangian Time Stepping for Stochastic Optimal Control Problems with Application to the Valuation of Natural Gas Storage

We describe a semi-Lagrangian time-stepping algorithm for a particular class of stochastic optimal control problems, applicable to storage valuation problems. The discretization in time uses a semi-Lagrangian approach based on Strang splitting, and convergence to the unique viscosity solution is established by appealing to the framework of Barles and Souganidis [Asymptotic Anal., 4 (1991), pp. 271--283]. The approach is illustrated in the context of a natural gas storage setting. A fully discrete approximation for the storage valuation problem using a Fourier-cosine method is described, and second-order convergence demonstrated, for pure-diffusion and jump-diffusion models. [PUBLICATION ABSTRACT]