scholarly journals Diversification Benefits Under Multivariate Second Order Regular Variation

2017 ◽  
Author(s):  
Bikramjit Das ◽  
Marie Kratz
Keyword(s):  
Regular Variation ◽  
Second Order ◽  
Second Order Regular Variation

scholarly journals Risk concentration under second order regular variation

Extremes ◽  
2020 ◽  
Vol 23 (3) ◽  
pp. 381-410
Author(s):  
Bikramjit Das ◽  
Marie Kratz
Keyword(s):  
Regular Variation ◽  
Second Order ◽  
Second Order Regular Variation

PROPERTIES OF SECOND-ORDER REGULAR VARIATION AND EXPANSIONS FOR RISK CONCENTRATION

2012 ◽  
Vol 26 (4) ◽  
pp. 535-559 ◽  
Author(s):  
Wenhua Lv ◽  
Tiantian Mao ◽  
Taizhong Hu
Keyword(s):  
Regular Variation ◽  
Generalized Inverse ◽  
Random Variables ◽  
Heavy Tail ◽  
Second Order ◽  
Tail Probabilities ◽  
Inverse Transform ◽  
Second Order Regular Variation ◽  
Independent And Identically Distributed

The purpose of this study is two-fold. First, we investigate further properties of the second-order regular variation (2RV). These properties include the preservation properties of 2RV under the composition operation and the generalized inverse transform, among others. Second, we derive second-order expansions of the tail probabilities of convolutions of non-independent and identically distributed (i.i.d.) heavy-tail random variables, and establish second-order expansions of risk concentration under mild assumptions. The main results extend some ones in the literature from the i.i.d. case to non-i.i.d. case.

THE SECOND-ORDER REGULAR VARIATION OF ORDER STATISTICS

2013 ◽  
Vol 28 (2) ◽  
pp. 209-222 ◽  
Author(s):  
Qing Liu ◽  
Tiantian Mao ◽  
Taizhong Hu
Keyword(s):  
Distribution Function ◽  
Order Statistics ◽  
Regular Variation ◽  
Random Variables ◽  
Second Order ◽  
Tail Probabilities ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Second Order Regular Variation ◽  
Independent And Identically Distributed

Let X1, …, Xn be non-negative, independent and identically distributed random variables with a common distribution function F, and denote by X1:n ≤ ··· ≤ Xn:n the corresponding order statistics. In this paper, we investigate the second-order regular variation (2RV) of the tail probabilities of Xk:n and Xj:n − Xi:n under the assumption that $\bar {F}$ is of the 2RV, where 1 ≤ k ≤ n and 1 ≤ i < j ≤ n.

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