On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications

By Jun Cai, Qihe Tang. Journal of Applied Probability, 2004

97 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4341ec0502ba15e304c7d7720b18d99143a0bc55

How researchers see this paper

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

In Finance

1. Yiqing Chen
2. Dingcheng Wang
3. Kai Wang Ng
4. Kam Chuen Yuen
5. Qihe Tang
6. C. Su
7. Shijie Wang
8. Bangwon Ko

In Management Science and Operations Research

1. Kam Chuen Yuen
2. Yiqing Chen
3. Qihe Tang
4. Dingcheng Wang
5. Kai Wang Ng
6. C. Su
7. Shijie Wang
8. Yong Zeng

In Statistics and Probability

1. Kai Wang Ng
2. Qihe Tang
3. Hailiang Yang
4. Yiqing Chen
5. Yong Zeng
6. Kam Chuen Yuen

Citations in the corpus

• Precise large deviations for sums of random variables with consistently varying tails (2004, background): “Cline and Samorodnitsky (1994, p. 87) constructed some examples to show that C is strictly larger than ERV and that D ∩ S is strictly larger than C. Related discussions can also be found in Cai and Tang (2004).”
• Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation (2009, background): “It is well-known that ⊂ ERV ⊂ ⊂ Moreover, Cai and Tang[3] and Cline and Samorodnitsky[5] gave nontrivial examples showing that the class is strictly larger than the class .”
• SUMS OF DEPENDENT NONNEGATIVE RANDOM VARIABLES WITH SUBEXPONENTIAL TAILS (2008, background): “The first integral in the bracket is asymptotically equal to F1(x) + F2(x); for case (i), see Corollary 1 of Cline (1986) while, for case (ii), see Theorem 2.1 of Cai and Tang (2004).”
• Asymptotics for Risk Capital Allocations Based on Conditional Tail Expectation (2011, unknown): “4) is included in Charpentier and Segers (2009). The vast majority of Archimedean copulae that satisfy (4.”
• Insensitivity to Negative Dependence of the Asymptotic Behavior of Precise Large Deviations (2006, methodology): “Clearly, the class C covers the class R. Examples that illustrate the inclusion R ⊂ C is proper were given in Cline and Samorodnitsky (1994) and Cai and Tang (2004).”
• Precise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-Risk Models (2007, background): “By Theorem 2.2 of Cai and Tang (2004), if Fi ∈ C then Fni∗i ∈ C.”
• Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory (2005, background): “In fact, Cai and Tang [ 10 ] showed that the class C is strictly larger than the class R.”