Search results for "Optimal stopping rule"
showing 3 items of 3 documents
Optimal selection of the four best of a sequence
1993
We consider the situation in which the decision-maker is allowed to have four choices with purpose to choose exactly the four absolute best candidates fromN applicants. The optimal stopping rule and the maximum probability of making the right choice are given for largeN∈N, the maximum asymptotic value of the best choice being limN→∞P(win)≈0.12706.
The best choice problem with an unknown number of objects
1993
The secretary problem with a known prior distribution of the number of candidates is considered. Ifp(i)=p(N=i),i ∈ [α, β] ∩ ℕ, whereα=inf{i ∈ℕ:p(i) > 0} andβ=sup{i ∈ℕ:p(i)≳0}, is the prior distribution of the numberN of candidates it will be shown that, if the optimal stopping rule is of the simple form, then the optimal stopping indexj=minΓ satisfies asymptotically (asβ → ∞) the equationj=exp $${{\left[ {\left( {\sum\limits_{i = max(\alpha ,j)}^\beta {p(i) \log (i)/i} } \right)} \right]} \mathord{\left/ {\vphantom {{\left[ {\left( {\sum\limits_{i = max(\alpha ,j)}^\beta {p(i) \log (i)/i} } \right)} \right]} {\left. {\left( {\sum\limits_{i = max(\alpha ,j)}^\beta {p(i)/i} } \right) - 1} \ri…
Optimal selection of thek best of a sequence withk stops
1997
We first consider the situation in which the decision-maker is allowed to have five choices with purpose to choose exactly the five absolute best candidates fromN applicants. The optimal stopping rule and the maximum probability of making the right five-choice are given for largeN eN, the maximum asymptotic value of the probability of the best choice being limN→∝P (win) ≈ 0.104305. Then, we study the general problem of selecting thek best of a sequence withk stops, constructing first a rough solution for this problem. Using this suboptimal solution, we find an approximation for the optimal probability valuesPk of the form $$P_k \approx \frac{1}{{(e - 1)k + 1}}$$ for any k eN.