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\footnotesize
\noindent Statistica Sinica {\bf 17}(2007), 725-733

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\centerline{\large\bf STOPPING AT THE LAST RENEWAL UP TO}
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\centerline{\large\bf  A TERMINAL TIME}
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\author{Shoou-Ren Hsiau}
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\centerline{\it National Changhua University of Education}
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\begin{quotation}
\noindent {\it 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).\par \vspace{9pt} \noindent {\it Key words and phrases:} Last
renewal, monotone case, optimal stopping rule, renewal process. \par
\end{quotation}

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