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Mathematical statistics --- Sequential analysis --- Optimal stopping (Mathematical statistics) --- 51 --- Statistical decision --- Stopping, Optimal (Mathematical statistics) --- Mathematics --- 51 Mathematics --- Statistique mathématique --- Analyse séquentielle --- Sequential analysis. --- Analyse séquentielle. --- Statistique mathématique --- Analyse séquentielle.

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Although three decades have passed since first publication of this book reprinted now as a result of popular demand, the content remains up-to-date and interesting for many researchers as is shown by the many references to it in current publications. The "ground floor" of Optimal Stopping Theory was constructed by A.Wald in his sequential analysis in connection with the testing of statistical hypotheses by non-traditional (sequential) methods. It was later discovered that these methods have, in idea, a close connection to the general theory of stochastic optimization for random processes. The area of application of the Optimal Stopping Theory is very broad. It is sufficient at this point to emphasise that its methods are well tailored to the study of American (-type) options (in mathematics of finance and financial engineering), where a buyer has the freedom to exercise an option at any stopping time. In this book, the general theory of the construction of optimal stopping policies is developed for the case of Markov processes in discrete and continuous time. One chapter is devoted specially to the applications that address problems of the testing of statistical hypotheses, and quickest detection of the time of change of the probability characteristics of the observable processes. The author, A.N.Shiryaev, is one of the leading experts of the field and gives an authoritative treatment of a subject that, 30 years after original publication of this book, is proving increasingly important.

Optimal stopping (Mathematical statistics) --- Sequential analysis. --- Mathematical statistics --- Statistical decision --- Stopping, Optimal (Mathematical statistics) --- Sequential analysis --- Distribution (Probability theory. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Statistics . --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk

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Game theory --- Optimal stopping (Mathematical statistics) --- Mathematical statistics --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Stopping, Optimal (Mathematical statistics) --- Sequential analysis --- Games, Theory of --- Theory of games --- Mathematical models --- Statistical methods --- Théorie des jeux --- Arrêt optimal (Statistique mathématique) --- Statistique mathématique --- Ferguson, Thomas S.

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This is a concise and elementary introduction to stochastic control and mathematical modelling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Contents include the basics of analysis and probability, the theory of stochastic differential equations, variational problems, problems in optimal consumption and in optimal stopping, optimal pollution control, and solving the Hamilton-Jacobi-Bellman (HJB) equation with boundary conditions. Major mathematical prerequisites are contained in the preliminary chapters or in the appendix so that readers can proceed without referring to other materials.

Stochastic control theory --- Optimal stopping (Mathematical statistics) --- Stochastic differential equations --- 519.2 --- 629.8312 --- 303.0 --- 305.976 --- 330.3 --- AA / International- internationaal --- Differential equations --- Fokker-Planck equation --- Control theory --- Stochastic processes --- Stopping, Optimal (Mathematical statistics) --- Sequential analysis --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken) --- Algoritmen. Optimisatie --- Methode in staathuishoudkunde. Statische, dynamische economie. Modellen. Experimental economics --- Stochastic control theory. --- Stochastic differential equations. --- Mathematical Sciences --- Probability

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The present monograph, based mainly on studies of the authors and their - authors, and also on lectures given by the authors in the past few years, has the following particular aims: To present basic results (with proofs) of optimal stopping theory in both discrete and continuous time using both martingale and Mar- vian approaches; To select a seriesof concrete problems ofgeneral interest from the t- ory of probability, mathematical statistics, and mathematical ?nance that can be reformulated as problems of optimal stopping of stochastic processes and solved by reduction to free-boundary problems of real analysis (Stefan problems). The table of contents found below gives a clearer idea of the material included in the monograph. Credits and historical comments are given at the end of each chapter or section. The bibliography contains a material for further reading. Acknowledgements.TheauthorsthankL.E.Dubins,S.E.Graversen,J.L.Ped- sen and L. A. Shepp for useful discussions. The authors are grateful to T. B. To- zovafortheexcellenteditorialworkonthemonograph.Financialsupportandh- pitality from ETH, Zur ¨ ich (Switzerland), MaPhySto (Denmark), MIMS (Man- ester) and Thiele Centre (Aarhus) are gratefully acknowledged. The authors are also grateful to INTAS and RFBR for the support provided under their grants. The grant NSh-1758.2003.1 is gratefully acknowledged. Large portions of the text were presented in the “School and Symposium on Optimal Stopping with App- cations” that was held in Manchester, England from 17th to 27th January 2006.

Optimal stopping (Mathematical statistics) --- Boundary value problems. --- Nonlinear integral equations. --- Economics, Mathematical. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Methodology --- Integral equations, Nonlinear --- Integral equations --- Nonlinear theories --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Stopping, Optimal (Mathematical statistics) --- Sequential analysis --- Optimal stopping (Mathematical statistics). --- Boundary value problems --- Nonlinear integral equations --- Economics, Mathematical --- Arrêt optimal (Statistique mathématique) --- Problèmes aux limites --- Equations intégrales non linéaires --- Mathématiques économiques --- EPUB-LIV-FT SPRINGER-B LIVMATHE --- Distribution (Probability theory. --- Mathematical optimization. --- Differential equations, partial. --- Finance. --- Probability Theory and Stochastic Processes. --- Calculus of Variations and Optimal Control; Optimization. --- Partial Differential Equations. --- Quantitative Finance. --- Funding --- Funds --- Currency question --- Partial differential equations --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Calculus of variations. --- Partial differential equations. --- Economics, Mathematical . --- Isoperimetrical problems --- Variations, Calculus of --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk