Article ID: | iaor20116789 |
Volume: | 22 |
Issue: | 3 |
Start Page Number: | 231 |
End Page Number: | 252 |
Publication Date: | Jun 2011 |
Journal: | IMA Journal of Management Mathematics |
Authors: | Howell Sydney D, Duck Peter W, Hazel Andrew, Johnson Paul V, Pinto Helena, Strbac Goran, Proudlove Nathan, Black Mary |
Analytic solutions exist only for highly idealized simple problems in stochastic storage; while simulation is available for complex problems, it is generally impractically slow. In this paper, a system of partial differential equations (PDEs), based on a novel combination of the techniques used to value options in finance, is developed and shown to efficiently value stochastic storage. The PDE system requires somewhat non‐standard (but well‐defined) numerical solution methods, which are up to nine orders of magnitude faster than simulation (and yet yields the same results). These faster calculations should permit better analysis of system design and operating procedures (including optimization) for a large set of problems in physical and financial stochastic storage. The motivation for this work is in the management of significant amounts of wind‐generated electricity into a power system, in particular by smoothing out random fluctuations in supply.