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.
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