A refined and asymptotic analysis of optimal stopping problems of Bruss and Weber
Journal Title: Mathematica Applicanda. Annales Societatis Mathematicae Polonae Series III . - Year 2017, Vol 45, Issue 1
Abstract
The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. The Bruss-Weber problems we consider center around the following model: Let X1,X2, . . . ,Xn be a sequence of independent and identically distributed random variables which can take three values: {+1,−1, 0}. The goal is to maximize the probability of stopping on a value +1 or −1 appearing for the last time in the sequence. We study related problems both in discrete and continuous time settings, with known or unknown number of observations, and known and unknown probability measure. In particular, so called x-strategy with incomplete information is taken into consideration. Our contribution in the present paper is a refined analysis of several problems in this class and a study of the asymptotic behaviour of solutions. We also present simulations of the corresponding complete selection algorithms.
Authors and Affiliations
Guy Louchard
Keywords
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- EP ID EP420944
- DOI 10.14708/ma.v45i2.4376
- Views 94
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