Format:
Online-Ressource (XVI, 388p. 24 illus, digital)
ISBN:
9783642183249
Series Statement:
Universitext
Content:
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.
Content:
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). .
Note:
Includes bibliographical references and index
,
""Markov Decision Processeswith Applications to Finance""; ""Preface""; ""Contents""; ""List of Symbols""; ""Chapter 1: Introduction and First Examples""; ""1.1 Applications""; ""1.2 Organization of the Book""; ""1.3 Notes and References""; ""Part I Finite Horizon Optimization Problems and Financial Markets""; ""Chapter 2: Theory of Finite Horizon Markov Decision Processes""; ""2.1 Markov Decision Models""; ""2.2 Finite Horizon Markov Decision Models""; ""2.3 The Bellman Equation""; ""2.4 Structured Markov Decision Models""; ""2.4.1 Semicontinuous Markov Decision Models""
,
""2.4.2 Continuous Markov Decision Models""""2.4.3 Measurable Markov Decision Models""; ""2.4.4 Monotone and Convex Markov Decision Models""; ""2.4.5 Comparison of Markov Decision Models""; ""2.5 Stationary Markov Decision Models""; ""2.6 Applications and Examples""; ""2.6.1 Red-and-Black Card Game""; ""2.6.2 A Cash Balance Problem""; ""2.6.3 Stochastic Linear-Quadratic Problems""; ""2.7 Exercises""; ""2.8 Remarks and References""; ""Chapter 3: The Financial Markets ""; ""3.1 Asset Dynamics and Portfolio Strategies ""; ""3.2 Jump Markets in Continuous Time""
,
""3.3 Weak Convergence of Financial Markets""""3.4 Utility Functions and Expected Utility""; ""3.5 Exercises""; ""3.6 Remarks and References""; ""Chapter 4: Financial Optimization Problems""; ""4.1 The One-Period Optimization Problem""; ""4.2 Terminal Wealth Problems""; ""4.3 Consumption and Investment Problems""; ""4.4 Optimization Problems with Regime Switching""; ""4.5 Portfolio Selection with Transaction Costs""; ""4.6 Dynamic Mean-Variance Problems""; ""4.7 Dynamic Mean-Risk Problems""; ""4.8 Index-Tracking""; ""4.9 Indifference Pricing""; ""4.10 Approximation of Continuous-Time Models""
,
""4.11 Remarks and References""""Part II Partially Observable Markov Decision Problems""; ""Chapter 5: Partially Observable Markov Decision Processes""; ""5.1 Partially Observable Markov Decision Processes""; ""5.2 Filter Equations""; ""5.3 Reformulation as a Standard Markov Decision Model""; ""5.4 Bayesian Decision Models""; ""5.5 Bandit Problems with Finite Horizon""; ""5.6 Exercises""; ""5.7 Remarks and References""; ""Chapter 6: Partially Observable Markov Decision Problems in Finance""; ""6.1 Terminal Wealth Problems""; ""6.2 Dynamic Mean-Variance Problems""
,
""6.3 Remarks and References""""Part III Infinite Horizon Optimization Problems""; ""Chapter 7: Theory of Infinite Horizon Markov Decision Processes""; ""7.1 Markov Decision Models with Infinite Horizon""; ""7.2 Semicontinuous Markov Decision Models""; ""7.3 Contracting Markov Decision Models""; ""7.4 Positive Markov Decision Models""; ""7.5 Computational Aspects""; ""7.5.1 Howard's Policy Improvement Algorithm""; ""7.5.2 Linear Programming""; ""7.5.3 State Space Discretization""; ""7.6 Applications and Examples""; ""7.6.1 Markov Decision Models with Random Horizon""
,
""7.6.2 A Cash Balance Problem with Infinite Horizon ""
Additional Edition:
ISBN 9783642183232
Additional Edition:
Buchausg. u.d.T. Bäuerle, Nicole Markov decision processes with applications to finance Berlin, Heidelberg [u.a.] : Springer, 2011 ISBN 3642183239
Additional Edition:
ISBN 9783642183232
Language:
English
Subjects:
Mathematics
Keywords:
Markov-Entscheidungsprozess
;
Finanzmathematik
;
Markov-Entscheidungsprozess
;
Finanzmathematik
DOI:
10.1007/978-3-642-18324-9
URL:
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URL:
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