Optimal control of Markovian jump processes with different information structures [Elektronische Ressource] / vorgelegt von Jens Thorsten Winter

Optimal Controlof Markovian Jump Processeswith Different Information StructuresOptimal Control of Markovian JumpProcesses with Different InformationStructuresDissertationzur Erlangung des Doktorgrades Dr. rer. nat.der Fakult¨at fu¨r Mathematik und Wirtschaftswissenschaftender Universit¨at Ulmvorgelegt vonJens Thorsten Winter2008iiAmtierender Dekan: Prof. Dr. Frank StehlingErstgutachter: Prof. Dr. Ulrich RiederZweitgutachter: Prof. Dr. Dieter KalinTag der Promotion: 15. Oktober 2008Contents iiiContents1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Contributions of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Structure of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 The Incomplete Information Model 62.1 Construction of the Processes . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Admissible Controls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 The Optimization Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 The Reduction to a Model with Complete Information 183.1 Filter Equation for the Unobservable Process . . . . . . . . . . . . . . . . . 203.2 The Reduced Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 Solving the Reduced Model 354.1 The Generalized HJB-Equation and Verification Technique . . . . . . . . . 364.2 Solution via a Transformed MDP . . . . . . . . . . . .