The subexponentiality of products revisited

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Randomly weighted sums of subexponential random variables with application to capital allocation (2014, background): “(10) As shown in Corollary 2.1 of Tang (2006), either one of the following is sufficient for (9) to hold: • P (θi > xy) = o ( Fi(x) ) for some y > 0; • P (θi > xy) = o(1)P (θi > x) for some y > 1; • 0 < M∗ (Gi) ≤ ∞ and E [( X+i )βi ] = ∞ for some 0 < βi < M∗ (Gi), where Gi is the distribution…”
From light tails to heavy tails through multiplier (2008, background): “Recent studies on these classes are found in Pakes (2004), Shimura and Watanabe (2005), Tang (2006a), Su and Chen (2006), and Foss and Korshunov (2007), among others.”
Asymptotics of random contractions (2010, methodology): “Recent results on the subexponentiality of products are obtained in Tang (2006, 2008), Liu and Tang (2010).”