  We discuss two distinct approaches, for distorting risk measures of sums of
dependent random variables, which preserve the property of coherence. The
first, based on distorted expectations, operates on the survival function of
the sum. The second, simultaneously applies the distortion on the survival
function of the sum and the dependence structure of risks, represented by
copulas. Our goal is to propose risk measures that take into account the
fluctuations of losses and possible correlations between risk components.
