The Annals of Probability

Transitivity in Problems of Optimal Stopping

Albrecht Irle

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Abstract

In a sequential decision problem it is usually assumed that the available information is represented by an increasing family $\mathscr{F}$ of $\sigma$-algebras. Often a reduction, e.g., according to principles of sufficiency or invariance, is performed which yields a smaller family $\mathscr{G}$. The consequences of such a reduction for problems of optimal stopping are treated in this paper. It is shown that $\mathscr{G}$ is transitive for $\mathscr{F}$ (in the Bahadur sense) if and only if for any stochastic process adapted to $\mathscr{G}$ the value (i.e., maximal reward by optimal stopping) under $\mathscr{G}$ and the value under $\mathscr{F}$ are equal.

Article information

Source
Ann. Probab., Volume 9, Number 4 (1981), 642-647.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994369

Digital Object Identifier
doi:10.1214/aop/1176994369

Mathematical Reviews number (MathSciNet)
MR624690

Zentralblatt MATH identifier
0469.60039

JSTOR
links.jstor.org

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Stopping times optimal stopping transitivity

Citation

Irle, Albrecht. Transitivity in Problems of Optimal Stopping. Ann. Probab. 9 (1981), no. 4, 642--647. doi:10.1214/aop/1176994369. https://projecteuclid.org/euclid.aop/1176994369


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