Discretisation of continuous time stochastic optimal control problems with delay [Elektronische Ressource] / vorgelegt von Markus Fischer

Inaugural - DissertationzurErlangung der DoktorwürdederNaturwissenschaftlich-Mathematischen GesamtfakultätderRuprecht-Karls-UniversitätHeidelbergvorgelegt vonDiplom-MathematikerMarkus Fischeraus BerlinDatum (Tag der mündlichen Prüfung): 20. November 2007Discretisation of continuous-time stochasticoptimal control problems with delayProf. Dr. Markus ReißGutachter:Universität HeidelbergProf. Salah-Eldin A. MohammedSouthern Illinois University, CarbondaleiAbstractInthepresentwork,westudydiscretisationschemesforcontinuous-timestochasticoptimalcontrolproblemswithtimedelay.Thedynamicsofthecontrolproblemstobeapproximatedaredescribedbycontrolledstochasticdelay(orfunctional)differentialequations.Thevaluefunctions associated with such control problems are defined on an infinite-dimensionalfunction space.The discretisation schemes studied are obtained by replacing the original control pro-blem by a sequence of approximating discrete-time Markovian control problems with finiteor finite-dimensional state space. Such a scheme is convergent if the value functions as-sociated with the approximating control problems converge to the value function of theoriginal problem.Following a general method for the discretisation of continuous-time control problems,sufficient conditions for the convergence of discretisation schemes for a class of stochasticoptimal control problems with delay are derived. The general method itself is cast in aformal framework.