Running minimum in the best-choice problem

Author:

Gnedin Alexander,Kozieł Patryk,Sulkowska MałgorzataORCID

Abstract

AbstractThe full-information best choice problem asks one to find a strategy maximising the probability of stopping at the minimum (or maximum) of a sequence $$X_1,\cdots ,X_n$$ X 1 , , X n of i.i.d. random variables with continuous distribution. In this paper we look at more general models, where independent $$X_j$$ X j ’s may have different distributions, discrete or continuous. A central role in our study is played by the running minimum process, which we first employ to re-visit the classic problem and its limit Poisson counterpart. The approach is further applied to two explicitly solvable models: in the first the distribution of the jth variable is uniform on $$\{j,\cdots ,n\}$$ { j , , n } , and in the second it is uniform on $$\{1,\cdots , n\}$$ { 1 , , n } .

Funder

Wroclaw University of Science and Technology subsidy

Publisher

Springer Science and Business Media LLC

Subject

Economics, Econometrics and Finance (miscellaneous),Engineering (miscellaneous),Statistics and Probability

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