Characterizing Asymptotic Dependence via Conditional Kendall's Tau

Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the "one-jump" property of the risk model. Non-trivial limits are obtained when the dependence among the first two order statistics is considered. Our results help in understanding the extreme behaviour of well-known reinsurance treaties that involve only few large claims. Interestingly, the Pearson product-moment correlation coefficient between the first two order statistics provides an alternative procedure to estimate the tail index of the underlying distribution.

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“…ii) It holds for every m, n, k ≥ 2 that lim t→∞ Pr X (1) m > Y (1) n , X (2) m > Z (2) r |X (2) m , Y (2) n , Z (2) r > t = 13 45 .…”

Section: Main Results: Spearman's Rhomentioning

confidence: 99%

“…∞]2 , where the probability measureµ + (x, ∞] × (y, ∞] = max(x, y) −α .For every fixed ξ > 0, let D ξ := {xy > ξ}. Since µ + (∂D ξ ) = 0, the latter shows that lim t→∞ Pr SX(1) …”

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confidence: 99%

Asymptotic Results for Conditional Measures of Association of a Random Sum

Asimit

Chen

2014

SSRN Journal

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“…the joint tail behaviour, among various order statistics has been recently investigated in Hashorva (2007), Albrecher et al (2014) and Peng (2014). A recent paper, namely, Asimit et al (2014), studied the asymptotic behaviour of the conditional Kendall's tau from a statistical extremes perspective. The latter paper and current one lead to a conclusive assertion that conditional measures of association are useful in understanding individual and concomitant rare events.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic results for conditional measures of association of a random sum

Asimit¹,

Chen²

2015

Insurance: Mathematics and Economics

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h i g h l i g h t s• The extreme behaviour of several conditional measures of association is investigated. • Many of the results have confirmed the ''one-jump'' property of the risk model. • A new tail index estimator is found whenever the Pearson product-moment correlation coefficient between the first two order statistics is chosen. a b s t r a c tAsymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the ''one-jump'' property of the risk model. Non-trivial limits are obtained when the dependence among the first two order statistics is considered. Our results help in understanding the extreme behaviour of well-known reinsurance treaties that involve only few large claims. Interestingly, the Pearson product-moment correlation coefficient between the first two order statistics provides an alternative procedure to estimate the tail index of the underlying distribution.

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On the worst and least possible asymptotic dependence

Asimit

Gerrard

2016

Journal of Multivariate Analysis

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Characterizing Asymptotic Dependence via Conditional Kendall's Tau

Cited by 3 publications

References 30 publications

Asymptotic Results for Conditional Measures of Association of a Random Sum

Asymptotic Results for Conditional Measures of Association of a Random Sum

Asymptotic results for conditional measures of association of a random sum

On the worst and least possible asymptotic dependence

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