Max-stable random sup-measures with comonotonic tail dependence. (English) Zbl 1346.60072
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.
MSC:
| 60G70 | Extreme value theory; extremal stochastic processes |
| 60G57 | Random measures |
| 60D05 | Geometric probability and stochastic geometry |
| 91B30 | Risk theory, insurance (MSC2010) |
Keywords:
extremes; random sup-measures; max-stability; capacity; tail dependence; Choquet integral; comonotonic additive functional; extremal coefficient; extremal integral; complete alternation; continuous choice; LePage series; random sets; risk measuresReferences:
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