Extreme value behavior of aggregate dependent risks

► We investigate properties of the limiting constants appearing in Alink et al. (2004). ► We revisit the asymptotic behavior of CTEs of aggregate risks for the Weibull and Gumbel cases. ► The main results complement some results in Alink et al. (2004, 2005), Barbe et al. (2006), and Embrechts et al. (2009).