Maxima of Sums of Heavy-Tailed Random Variables

By K. Ng, Q. Tang, H. Yang. ASTIN Bulletin: The Journal of the International Actuarial Association, 2002

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Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory (2003, unknown): “% & 3 " % *% %!”
Asymptotics of randomly stopped sums in the presence of heavy tails (2008, background): “The case where F is a dominated varying distribution was studied in [34] and [9].”
The Ruin Probability of a Discrete Time Risk Model under Constant Interest Rate with Heavy Tails (2004, background): “…theorem gives f0 F1(x y)F1(dy) F1(0)F1(x): Hence, it follows from (4.8) that g x F1(x y)F1(dy) F1(x); (4:9) Substituting (4.9) into (4.7) yields that F (x)+ (1 c o)F1(x): Relation (4.6) follows from the arbitrariness of o 0: The followingis the restatement of Theorem 2.1 in Ng et al. (2002).”
Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables (2009, background): “[25], while part (b) can be found in Embrechts and Goldie [8].”