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A new strategy for Robbins’ problem of optimal stopping

Part of: Stochastic processes

Published online by Cambridge University Press:  04 April 2017

Martin Meier  and
Leopold Sögner
Martin Meier*
Affiliation:
IHS Vienna
Leopold Sögner*
Affiliation:
IHS Vienna
*
* Postal address: Department of Economics and Finance, Institute for Advanced Studies, Josefstädter Straße 39, 1080 Vienna, Austria.
* Postal address: Department of Economics and Finance, Institute for Advanced Studies, Josefstädter Straße 39, 1080 Vienna, Austria.
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Abstract

In this paper we study the expected rank problem under full information. Our approach uses the planar Poisson approach from Gnedin (2007) to derive the expected rank of a stopping rule that is one of the simplest nontrivial examples combining rank dependent rules with threshold rules. This rule attains an expected rank lower than the best upper bounds obtained in the literature so far, in particular, we obtain an expected rank of 2.326 14.

Keywords

Optimal stoppingRobbins’ problem

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017 , pp. 331 - 336
Copyright
Copyright © Applied Probability Trust 2017 

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