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

Guy Louchard. "A refined and asymptotic analysis of optimal stopping problems of Bruss and Weber." Mathematica Applicanda 45.2 (2017): null. <http://eudml.org/doc/293202>.

@article{GuyLouchard2017,
abstract = {The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. The Bruss-Weber problems we consider center around the following model: Let X1;X2;... ;Xn be a sequence of independent and identically distributed random variables which can take three values: \{+1;-1; 0\}. The goal is to maximize the probability of stopping on a value +1 or -1 appearing for the last time in the sequence. We study related problems both in discrete and continuous time settings, with known or unknown number of observations, and known and unknown probability measure. In particular, so called x-strategy with incomplete information is taken into consideration. Our contribution in the present paper is a refined analysis of several problems in this class and a study of the asymptotic behaviour of solutions. We also present simulations of the corresponding complete selection algorithms.},
author = {Guy Louchard},
journal = {Mathematica Applicanda},
keywords = {Stopping times, Unied Approach to best choice, Odds-algorithm, Optimal solutions, x-Strategy, Asymptotic expansions, Incomplete information.},
language = {eng},
number = {2},
pages = {null},
title = {A refined and asymptotic analysis of optimal stopping problems of Bruss and Weber},
url = {http://eudml.org/doc/293202},
volume = {45},
year = {2017},
}

TY - JOUR
AU - Guy Louchard
TI - A refined and asymptotic analysis of optimal stopping problems of Bruss and Weber
JO - Mathematica Applicanda
PY - 2017
VL - 45
IS - 2
SP - null
AB - The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. The Bruss-Weber problems we consider center around the following model: Let X1;X2;... ;Xn be a sequence of independent and identically distributed random variables which can take three values: {+1;-1; 0}. The goal is to maximize the probability of stopping on a value +1 or -1 appearing for the last time in the sequence. We study related problems both in discrete and continuous time settings, with known or unknown number of observations, and known and unknown probability measure. In particular, so called x-strategy with incomplete information is taken into consideration. Our contribution in the present paper is a refined analysis of several problems in this class and a study of the asymptotic behaviour of solutions. We also present simulations of the corresponding complete selection algorithms.
LA - eng
KW - Stopping times, Unied Approach to best choice, Odds-algorithm, Optimal solutions, x-Strategy, Asymptotic expansions, Incomplete information.
UR - http://eudml.org/doc/293202
ER -