The Annals of Statistics

Stopping a Sum During a Success Run

Thomas S. Ferguson

Full-text: Open access

Abstract

Let $\{Z_i\}$ be i.i.d., let $\{\varepsilon_i\}$ be i.i.d. Bernoulli, independent of $\{Z_i\}$, let $T_0 = z$ and $T_n = \varepsilon_n(T_{n-1} + Z_n)$ for $n \geqq 1$. Under a moment condition, optimal stopping rules are found for stopping $T_n - nc$ where $c > 0$ (the cost model), and for stopping $\beta^nT_n$ where $0 < \beta < 1$ (the discount model). Special cases are treated in detail. The cost model generalizes results of N. Starr, and the discount model generalizes results of Dubins and Teicher.

Article information

Source
Ann. Statist., Volume 4, Number 2 (1976), 252-264.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343405

Digital Object Identifier
doi:10.1214/aos/1176343405

Mathematical Reviews number (MathSciNet)
MR408144

Zentralblatt MATH identifier
0324.62062

JSTOR
links.jstor.org

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

Keywords
Optimal stopping rules cost model discount model principle of optimality

Citation

Ferguson, Thomas S. Stopping a Sum During a Success Run. Ann. Statist. 4 (1976), no. 2, 252--264. doi:10.1214/aos/1176343405. https://projecteuclid.org/euclid.aos/1176343405


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