The theory of Markov decision processes focuses on controlled Markov chains in discrete time. The authors establish the theory for general state and action spaces and at the same time show its application by means of numerous examples, mostly taken from the fields of finance and operations research. By using a structural approach many technicalities (concerning measure theory) are avoided. They cover problems with finite and infinite horizons, as well as partially observable Markov decision processes, piecewise deterministic Markov decision processes and stopping problems.

The book presents Markov decision processes in action and includes various state-of-the-art applications with a particular view towards finance. It is useful for upper-level undergraduates, Master's students and researchers in both applied probability and finance, and provides exercises (without solutions).

Autorentext

Nicole Bäuerle is full professor for Stochastics at the Karlsruhe Institute of Technology. Currently she is in the board of the Fachgruppe Stochastik and the DGVFM (Deutsche Gesellschaft für Versicherungs- und Finanzmathematik). She is editor of the journals "Stochastic Models" and "Mathematical Methods of Operations Research".

Ulrich Rieder is full professor for Optimization and Operations Research at the University of Ulm since 1980. He helped to establish a new program in applied mathematics at Ulm, called Wirtschaftsmathematik. From 1990-2008 he was editor-in-chief of "Mathematical Methods of Operations Research". He is editor of several journals in the areas of operations research and finance.

Inhalt

Preface.- 1.Introduction and First Examples.- Part I Finite Horizon Optimization Problems and Financial Markets.- 2.Theory of Finite Horizon Markov Decision Processes.- 3.The Financial Markets.- 4.Financial Optimization Problems.- Part II Partially Observable Markov Decision Problems.- 5.Partially Observable Markov Decision Processes.- 6.Partially Observable Markov Decision Problems in Finance.- Part III Infinite Horizon Optimization Problems.- 7.Theory of Infinite Horizon Markov Decision Processes.- 8.Piecewise Deterministic Markov Decision Processes.- 9.Optimization Problems in Finance and Insurance.- Part IV Stopping Problems.- 10.Theory of Optimal Stopping Problems.- 11.Stopping Problems in Finance.- Part V Appendix.- A.Tools from Analysis.- B.Tools from Probability.- C.Tools from Mathematical Finance.- References.- Index.