Stochastic maximum principle for optimal control under uncertainty

Abstract

Optimal control problems involve the difficult task of determining time-varying profiles through dynamic optimization. Such problems become even more complex in practical situations where handling time dependent uncertainties becomes an important issue. Approaches to stochastic optimal control problems have been reported in the finance literature and are based on real option theory, combining Ito’s Lemma and the dynamic programming formulation. This paper describes a new approach to stochastic optimal control problems in which the stochastic dynamic programming formulation is converted into a stochastic maximum principle formulation. An application of such method has been reported by Rico-Ramirez et al. ( Computers and Chemical Engineering, 2003, 27, 1867) but no details of the derivation were provided. The main significance of this approach is that the solution to the partial differential equations involved in the dynamic programming formulation is avoided. The classical isoperimetric problem illustrates this approach.