Stochastic Control

Abstract

The purpose of this lecture is to survey the main aspects of stochastic control theory and its applications. To try to be exhaustive is impossible, since the applications are extremely diversified from engineering to management, statistics,…, and the methods make use of many disciplines such as functional analysis, partial differential equations, probability theory and stochastic processes, control theory and optimization, game theory, numerical analysis among the main ones. From the results point of view there are basically three parts. Firstly the situation of one (or several) decision maker with complete information, where the theory is well understood and several numerical algorithms exist. Secondly, the situation of one decision maker with partial information, where the general theory is understood, but is difficult to apply. There, progress has to be made in the search of particular cases where the solution simplifies, or in the search of more efficient algorithms, making use for instance of parallel processing. Finally, the case of several decision makers with partial information is widely open on the theory side, although some heuristic algorithms are available to handle practical applications.