Abstract: Given a renewal processand a fixed terminal time
, we want to find a strategy that maximizes the probability of stopping, without recall, at the last renewal up to
. We give a simple criterion to guarantee that the optimal strategy is of threshold type. This simple criterion is applied to several cases, including a problem of optimal stopping on patterns discussed in Bruss and Louchard (2003).
Key words and phrases: Last renewal, monotone case, optimal stopping rule, renewal process.