Multiple stopping odds problem in Bernoulli Trials with random number of observations

Abstract

This paper studies an optimal multiple stopping problem, in which the objective is to maximize the probability of selecting the last success on Bernoulli trials with random number of observations under multiple selections. We propose the sufficient condition on the probability distribution of the number of observations for the optimal multiple stopping rule to be a threshold rule which is characterized by odds. For example, uniform distribution satises the condition whenever the odd is not increasing in the number of trials.