Open Access
August, 1972 Optimal Stopping for Partial Sums
D. A. Darling, T. Liggett, H. M. Taylor
Ann. Math. Statist. 43(4): 1363-1368 (August, 1972). DOI: 10.1214/aoms/1177692491


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.


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D. A. Darling. T. Liggett. H. M. Taylor. "Optimal Stopping for Partial Sums." Ann. Math. Statist. 43 (4) 1363 - 1368, August, 1972.


Published: August, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0244.60037
MathSciNet: MR312564
Digital Object Identifier: 10.1214/aoms/1177692491

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 4 • August, 1972
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