The Annals of Mathematical Statistics

Optimal Stopping for Partial Sums

D. A. Darling, T. Liggett, and H. M. Taylor

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Abstract

We determine $\sup E\lbrack r(S_T)\rbrack$, where $S_n$ is a sequence of partial sums of independent identically distributed random variables, for two reward functions: $r(x) = x^+$ and $r(x) = (e^x - 1)^+$. The supremum is taken over all stop rules $T$. We give conditions under which the optimal expected return is finite. Under these conditions, optimal stopping times exist, and we determine them. The problem has an interpretation in an action timing problem in finance.

Article information

Source
Ann. Math. Statist., Volume 43, Number 4 (1972), 1363-1368.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692491

Digital Object Identifier
doi:10.1214/aoms/1177692491

Mathematical Reviews number (MathSciNet)
MR312564

Zentralblatt MATH identifier
0244.60037

JSTOR
links.jstor.org

Citation

Darling, D. A.; Liggett, T.; Taylor, H. M. Optimal Stopping for Partial Sums. Ann. Math. Statist. 43 (1972), no. 4, 1363--1368. doi:10.1214/aoms/1177692491. https://projecteuclid.org/euclid.aoms/1177692491


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