 On an optimal stopping problem of Gusein-ZadeArthur Q. Frank and Stephen M. Samuels Stochastic Processes and their Applications, 1980, vol. 10, issue 3, 299-311 Abstract: We study the problem of selecting one of the r best of n rankable individuals arriving in random order, in which selection must be made with a stopping rule based only on the relative ranks of the successive arrivals. For each r up to r=25, we give the limiting (as n-->[infinity]) optimal risk (probability of not selecting one of the r best) and the limiting optimal proportion of individuals to let go by before being willing to stop. (The complete limiting form of the optimal stopping rule is presented for each r up to r=10, and for r=15, 20 and 25.) We show that, for large n and r, the optical risk is approximately (1-t*)r, where t*[approximate]0.2834 is obtained as the roof of a function which is the solution to a certain differential equation. The optimal stopping rule [tau]r,n lets approximately t*n arrivals go by and then stops 'almost immediately', in the sense that [tau]r,n/n-->t* in probability as n-->[infinity], r-->[infinity] Keywords: Secretary; problem; optimal; stopping; relative; ranks; best; choice; problems (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:10:y:1980:i:3:p:299-311 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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