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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).  .

Markov processes. --- Statistical decision. --- Markov processes --- Programming (Mathematics) --- Stochastic control theory --- Finance --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematical models --- Decision problems --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Economics, Mathematical. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Applications of Mathematics. --- Game theory --- Operations research --- Statistics --- Management science --- Stochastic processes --- Distribution (Probability theory. --- Finance. --- Math --- Science --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Stochastic control theory. --- Mathematical models. --- Economics, Mathematical . --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematical economics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology

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Dieses Lehrbuch bietet eine leicht verständliche Einführung in die moderne Finanzmathematik und erläutert grundlegende mathematische Konzepte der Optionsbewertung, der Portfolio-Optimierung und des Risikomanagements. Hierzu gehören die Preisbestimmung durch Arbitrageüberlegungen, die Preisbestimmung von amerikanischen Optionen über die Lösung optimaler Stopp-Probleme, die Bestimmung von optimalen Konsum- und Investitionsstrategien und Erwartungswert-Varianz Portfolios. Aktuelle Konzepte der Risikomessung wie Value at Risk und Expected Shortfall werden ebenso vorgestellt. Grundlagen in Stochastik und Optimierung reichen für das Verständnis der Inhalte aus, und zahlreiche Übungsaufgaben mit ausführlichen Lösungen sowie drei Anhänge erleichtern das Selbststudium. Die Autoren Prof. Dr. Nicole Bäuerle, Institut für Stochastik, Karlsruher Institut für Technologie Prof. Dr. Ulrich Rieder, Institut für Optimierung und Operations Research, Universität Ulm.

Economics, Mathematical . --- Statistics . --- Quantitative Finance. --- Statistics for Business, Management, Economics, Finance, Insurance.

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This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.

Mathematics. --- System theory. --- Operations research. --- Management science. --- Mathematical optimization. --- Probabilities. --- Operations Research, Management Science. --- Systems Theory, Control. --- Discrete Optimization. --- Probability Theory and Stochastic Processes. --- Systems theory. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Quantitative business analysis --- Management --- Problem solving --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Systems, Theory of --- Systems science --- Science --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Philosophy