Tail asymptotic of Weibull-type risks

With motivation from Arendarczyk and Debicki [Asymptotics of supremum distribution of a Gaussian process over a Weibullian time. Bernoulli. 2011;17:194-210], in this paper we derive the tail asymptotics of the product of two dependent Weibull-type risks, which is of interest in various statistical and applied probability problems. Our results extend some recent findings of Schlueter and Fischer [The weak tail dependence coefficient of the elliptical generalized hyperbolic distribution. Extremes. 2012;15:159-174] and Bose et al. [Product of exponentials and spectral radius of random k circulants. Annales de l'Institut Henri Poincare Probabilites et Statistiques. 2012;48:424-443].