Optimal Stopping RulesSpringer Science & Business Media, 23.09.2007 - 220 Seiten Along with conventional problems of statistics and probability, the - vestigation of problems occurring in what is now referred to as stochastic theory of optimal control also started in the 1940s and 1950s. One of the most advanced aspects of this theory is the theory of optimal stopping rules, the development of which was considerably stimulated by A. Wald, whose Sequential ~nal~sis' was published in 1947. In contrast to the classical methods of mathematical statistics, according to which the number of observations is fixed in advance, the methods of sequential analysis are characterized by the fact that the time at which the observations are terminated (stopping time) is random and is defined by the observer based on the data observed. A. Wald showed the advantage of sequential methods in the problem of testing (from independent obser- tions) two simple hypotheses. He proved that such methods yield on the average a smaller number of observations than any other method using fixed sample size (and the same probabilities of wrong decisions). Furth- more, Wald described a specific sequential procedure based on his sequ- tial probability ratio criterion which proved to be optimal in the class of all sequential methods. By the sequential method, as applied to the problem of testing two simple hypotheses, we mean a rule according to which the time at which the observations are terminated is prescribed as well as the terminal decision as to which of the two hypotheses is true. |
Inhalt
1 | |
Notes to Chapter 1 | 24 |
Notes to Chapter 2 | 111 |
Notes to Chapter 3 | 162 |
Notes to Chapter 4 | 207 |
215 | |
Häufige Begriffe und Wortgruppen
a-algebras assertions assume assumption B(AT belongs Borel Chapter clear coincide condition consider constructed convergence decision rule defined definition denote discrete distribution easily equal equation example excessive function exists fact finite fixed follows forms formulation function g(x Further g e B(A gain given Hence holds hypotheses immediately implies independent inequality inf{n inf{t introduce L(AT Lemma Let the function lim g(x lim lim limit lower majorant of g(x Markov process martingale max{g(x measurable methods object observation obtain obvious operator optimal stopping rules particular payoff s(x probability problem PROOF properties prove random variable regular relation Remark respect S)-optimal satisfied seen sequence sequential smallest excessive majorant solution statistics structure sufficient sup Msg(x testing Theorem theory values virtue virtue of Theorem x e E
Beliebte Passagen
Seite x - References to sources of new results as well as supplementary material can be found in the Notes at the end of each chapter.
Seite vii - He proved that such methods yield on the average a smaller number of observations than any other method using fixed sample size (and the same probabilities of wrong decisions).
Verweise auf dieses Buch
Numerical Methods for Stochastic Control Problems in Continuous Time Harold J. Kushner,Paul Dupuis Eingeschränkte Leseprobe - 2001 |
Introduction to Stochastic Calculus Applied to Finance, Second Edition Damien Lamberton,Bernard Lapeyre Eingeschränkte Leseprobe - 1996 |