A note on the full-information Poisson arrival selection problem

This note studies a Poisson arrival selection problem for the full-information case with an unknown intensity (gamma) 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 fullinformation case is not a monotone stopping problem.