Applicable stochastic control: From theory to practice
Stochastic control is defined as a unifying framework for treating multi- stage or multi-period optimization problems subject to stochastic disturbances. Few problems can be solved analytically however. For this reason there is an increased awareness that a broad range of techniques including stochastic approximations, perturbations techniques, Markov decision processes, simulation, etc. are an essential part of stochastic control kits. This paper provides both an outline of the techniques and the applications of stochastic control to management and business problems. A framework is first constructed providing an outline of the type of decision problems handled by stochastic control. A number of problems are then formulated and solved analytically. Subsequently, a review of numerical techniques and non-trivial problems are considered. Particularly, a multi-armed bandit problem and an option trading problem is formulated and stochastic control techniques applied. For the latter problem, it is shown that the decision to sell an option is a simple stopping time problem.
scientific article; zbMATH DE number 609640
scientific article