Prophet inequalities for products of non–negative random variables

Abstract

Stopping time and supremum comparisons known as “Prophet inequalities” are made for products of finite sequences of non–negative integrable random variables under various restrictions on the class of distributions governing these random variables. for example it is shown that for X0= constant > 0, and non-nagative integrable random variables, that the expected maximum of the product variables, that the expected maximum of the product sequence is no more that n+1 times the value of the product sequence when stopped by non-anticipating stopping times