  Considerable literature has been devoted to developing statistical
inferential results for risk measures, especially for those that are of the
form of L-functionals. However, practical and theoretical considerations have
highlighted quite a number of risk measures that are of the form of ratios, or
even more complex combinations, of two L-functionals. In the present paper we
call such combinations `coupled risk measures' and develop a statistical
inferential theory for them when losses follow heavy-tailed distributions. Our
theory implies -at a stroke- statistical inferential results for absolute and
relative distortion risk measures, weighted premium calculation principles, as
well as for many indices of economic inequality that have appeared in the
econometric literature.
