Max-stable random sup-measures with comonotonic tail dependence

Several objects in the Extremes literature are special instances of max-stable random sup-measures. This perspective opens connections to the theory of random sets and the theory of risk measures and makes it possible to extend corresponding notions and results from the literature with streamlined p...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 126; no. 9; pp. 2835 - 2859
Main Authors Molchanov, Ilya, Strokorb, Kirstin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2016
Subjects
Capacity
Choquet integral
Choquet random sup-measure
Comonotonic additive functional
Complete alternation
Continuous choice
Extremal coefficient
Extremal integral
LePage series
Max-stability
Random set
Sup-measure
Tail dependence
60D05
60G57
Choquet integral
60G70
Choquet random sup-measure
Continuous choice
Max-stability
Extremal integral
91B16
Capacity
Sup-measure
Comonotonic additive functional
Complete alternation
Random set
Tail dependence
Extremal coefficient
LePage series
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Summary:Several objects in the Extremes literature are special instances of max-stable random sup-measures. This perspective opens connections to the theory of random sets and the theory of risk measures and makes it possible to extend corresponding notions and results from the literature with streamlined proofs. In particular, it clarifies the role of Choquet random sup-measures and their stochastic dominance property. Key tools are the LePage representation of a max-stable random sup-measure and the dual representation of its tail dependence functional. Properties such as complete randomness, continuity, separability, coupling, continuous choice, invariance and transformations are also analysed.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2016.03.004