Statistica Sinica 17(2007), 725-733

STOPPING AT THE LAST RENEWAL UP TO

A TERMINAL TIME

Shoou-Ren Hsiau

National Changhua University of Education

Abstract: Given a renewal process $\{S_n \}_{n \geq 1}$ and a fixed terminal time $T>0$, we want to find a strategy that maximizes the probability of stopping, without recall, at the last renewal up to $T$. 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.