On risk dependence and mrl ordering

Recently, it was shown that as dependence among random variables increases their sum increases in the sense of increasing convex ordering. The present article assumes strong dependence among Bernoulli random variables. This dependence implies that the sum of the random variables increases in the mean residual life (mrl) order. This result is stronger than the previous result, since the mrl ordering implies the increasing convex ordering. We thus extend a result presented in Bäuerle and Müller [1998. Modelling and comparing dependencies in multivariable risk portfolios. ASTIN Bull. 28, 59-76].