A note on the full-information Poisson arrival selection problem

Abstract

This note studies a Poisson arrival selection problem for the full-information case with an unknown intensity λ which has a Gamma prior density G(r, 1/a), where a>0 and r is a natural number. For the no-information case with the same setting, the problem is monotone and the one-step look-ahead rule is an optimal stopping rule; in contrast, this note proves that the full-information case is not a monotone stopping problem.

The best choice problem with random arrivals: How to beat the 1/e-strategy

“…Concretely, for each k there will be a cutoff time a k when the strategy starts accepting a record. Optimality of such strategies has been studied in selection problems with random number of items [16,27,35]. Exploring this large class, we further construct counter-examples to the assertion of risk monotonicity relative to the stochastic ordering on distributions of the number of items (see Theorem 2.3 in [10], Equation (36) in [32], Equation (76) in [33]).…”