 Embedding optimal selection problems in a Poisson processF. Thomas Bruss and L. C. G. Rogers Stochastic Processes and their Applications, 1991, vol. 38, issue 2, 267-278 Abstract: We consider optimal selection problems, where the number N1 of candidates for the job is random, and the times of arrival of the candidates are uniformly distributed in [0, 1]. Such best choice problems are generally harder than the fixed-N counterparts, because there is a learning process going on as one observes the times of arrivals, giving information about the likely values of N1. In certain special cases, notably when N1 is geometrically distributed, it had been proved earlier that the optimal policy was of a very simple form; this paper will explain why these cases are so simple by embedding the process in a planar Poisson process from which all the requisite distributional results can be read off by inspection. Routine stochastic calculus methods are then used to prove the conjectured optimal policy. Keywords: record; processes; optimal; selection; martingales; stochastic; calculus; planar; Poisson; process (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:38:y:1991:i:2:p:267-278 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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