  Multivariate regular variation plays a role assessing tail risk in diverse
applications such as finance, telecommunications, insurance and environmental
science. The classical theory, being based on an asymptotic model, sometimes
leads to inaccurate and useless estimates of probabilities of joint tail
regions. This problem can be partly ameliorated by using hidden regular
variation [Resnick, 2002, Mitra and Resnick, 2010]. We offer a more flexible
definition of hidden regular variation that provides improved risk estimates
for a larger class of risk tail regions.
