Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory

By Qihe Tang, G. Tsitsiashvili. 2003

143 citations recorded by the source corpus.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/920c53f970b82ac9462c9af66e088acd6dfec9c4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Demography

In Finance

In Management Science and Operations Research

Citations in the corpus

Asymptotics for ruin probability of some negatively dependent risk models with a constant interest rate and dominatedly-varying-tailed claims ☆ (2010, unknown): “1 of Wang et al. (2006) for the lemma below.”
Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model (2007, background): “See Proposition 5.1 of Tang and Tsitsiashvili (2003).”
Finite-Time Ruin Probability with Heavy-Tailed Claims and Constant Interest Rate (2008, methodology): “Asmussen, S.; Kalashnikov, V.; Konstantinides, D.; Klüppelberg, C.; Tsitsiashvili, G.”
Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation (2009, background): “Theorem 5.1 of Tang and Tsitsiashvili[29] is a special case of Theorem 3.2.”
Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model (2010, background): “Let X1, . . . , Xn be i.i.d. random variables with common distribution F ∈ S. Recall Proposition 5.1 of Tang and Tsitsiashvili (2003), which shows that, for arbitrarily fixed 0 < a ≤ b < ∞, the relation Pr ( n∑ k=1 wkXk > x ) ∼ n∑ k=1 Pr(wkXk > x) (4.1) holds uniformly for (w1, . . . , wn) ∈ [a,…”
A uniform asymptotic estimate for discounted aggregate claims with subexponential tails (2008, background): “The proof can be given by going along the same lines of the proof of Proposition 5.1 of Tang and Tsitsiashvili (2003) with some obvious modifications.”
Randomly weighted sums of subexponential random variables with application to capital allocation (2014, background): “5.1 Proof of Theorem 1 Following the proof of Proposition 5.1 of Tang and Tsitsiashvili (2003b) with some obvious changes, we obtain Lemma 1 Let X1, . . . , Xn be n real-valued independent random variables, each distributed by Fi satisfying Fi ∈ L and Fi(x) F(x) for some F ∈ S and all i = 1, . . .…”
Asymptotics for Weighted Random Sums (2011, background): “Results for more general classes of heavy-tailed distributions but stronger conditions on the weights and N = n are given in [19] (for bounded weights) and [6] (for Ci = ∏i j=1 Yj and {Yj} ≥ 0 i.”
Tail Probabilities of Randomly Weighted Sums of Random Variables with Dominated Variation (2006, background): “Tang, Q.; Tsitsiashvili, G. Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments.”