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The classical secretary problem has been generalized over the years intoseveral directions. In this paper we confine our interest to thosegeneralizations which have to do with the more general problem of stopping on alast observation of a specific kind. We follow Dendievel, (where a bibliographycan be found) who studies several types of such problems, mainly initiated byBruss and Weber. Whether in discrete time or continuous time, whether allparameters are known or must be sequentially estimated, we shall call suchproblems simply "Bruss-Weber problems". Our contribution in the present paperis a refined analysis of several problems in this class and a study of theasymptotic behaviour of solutions.  The problems we consider center around the following model. Let$X_1,X_2,\ldots,X_n$ be a sequence of independent random variables which cantake three values: $\{+1,-1,0\}.$ Let $p:=\P(X_i=1), p':=\P(X_i=-1),\qt:=\P(X_i=0), p\geq p'$, where $p+p'+\qt=1$. The goal is to maximize theprobability of stopping on a value $+1$ or $-1$ appearing for the last time inthe sequence. Following a suggestion by Bruss, we have also analyzed anx-strategy with incomplete information: the cases $p$ known, $n$ unknown, then$n$ known, $p$ unknown and finally $n,p$ unknown are considered. We alsopresent simulations of the corresponding complete selection algorithm.

A refined and asymptotic analysis of optimal stopping problems of Bruss and Weber