Two theorems on optimal stopping with backward solicitation

Abstract

This paper deals with optimal stopping rules for a sampling process with uncertain recall, i.e. the probability that a past observation is currently available declines exponentially with the time elapsed since it was last observed. The main result of this paper is that for such sampling processes, and for any utility function, if a solicitation of a past observation incurs the same cost as a new draw, then it is never optimal to continue the sampling when the observation solicited is found to be available. This result applies to both bounded and unbounded sequential decision procedures.