The minimum of the expected value of the product of three random variables in the Fréchet class

Summary In this paper the minimum of the expected value of the product of three random variables is studied as their joint distribution function varies in the Fréchet class associated to the three given marginal distribution functions. The general problem is studied for three positive valued random variables and a lower bound for the minimum is provided. The case of three uniformly distributed random variables in 0, 1] is analyzed in more detail and an upper bound for the minimum is given. The Author conjectures that the distribution correspondent to the upper bound is a solution of the problem. Paper written with the contribution of MURST (funds 40%).