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

作者：Ware Antony^*

来源：SIAM Journal on Financial Mathematics, 2013, 4(1): 427-451.

DOI：10.1137/110853546

• stochastic optimal control
• semi-Lagrangian methods
• splitting methods
• Fourier methods
• storage valuation

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.

• 出版日期2013