A new strategy for Robbins' problem of optimal stopping

Abstract: In this article 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 non-trivial 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 2.32614.