1 results
Two-choice optimal stopping
- Part of
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- Journal:
- Advances in Applied Probability / Volume 36 / Issue 4 / December 2004
- Published online by Cambridge University Press:
- 01 July 2016, pp. 1116-1147
- Print publication:
- December 2004
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- Article
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Let Xn,…,X1 be independent, identically distributed (i.i.d.) random variables with distribution function F. A statistician, knowing F, observes the X values sequentially and is given two chances to choose Xs using stopping rules. The statistician's goal is to stop at a value of X as small as possible. Let
equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behaviour of the sequence 
for a large class of Fs belonging to the domain of attraction (for the minimum) 𝒟(Gα), where Gα(x) = [1 - exp(-xα)]1(x ≥ 0) (with 1(·) the indicator function). The results are compared with those for the asymptotic behaviour of the classical one-choice value sequence 
, as well as with the ‘prophet value’ sequence 
equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behaviour of the sequence 
for a large class of 
, as well as with the ‘prophet value’ sequence 
