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Max-stable random sup-measures with comonotonic tail dependence

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  • Molchanov, Ilya
  • Strokorb, Kirstin

Abstract

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.

Suggested Citation

  • Molchanov, Ilya & Strokorb, Kirstin, 2016. "Max-stable random sup-measures with comonotonic tail dependence," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2835-2859.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:9:p:2835-2859
    DOI: 10.1016/j.spa.2016.03.004
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    References listed on IDEAS

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    1. Ressel, Paul, 2011. "Monotonicity properties of multivariate distribution and survival functions -- With an application to Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 393-404, March.
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    4. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
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    2. Yuen, Robert & Stoev, Stilian & Cooley, Daniel, 2020. "Distributionally robust inference for extreme Value-at-Risk," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 70-89.
    3. Stoev, Stilian & Wang, Yizao, 2019. "Exchangeable random partitions from max-infinitely-divisible distributions," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 50-56.
    4. Hashorva Enkelejd, 2016. "Domination of sample maxima and related extremal dependence measures," Dependence Modeling, De Gruyter, vol. 6(1), pages 88-101, May.
    5. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    6. Steven N. Evans & Ilya Molchanov, 2018. "Polar Decomposition of Scale-Homogeneous Measures with Application to Lévy Measures of Strictly Stable Laws," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1303-1321, September.
    7. Clémençon, Stephan & Huet, Nathan & Sabourin, Anne, 2024. "Regular variation in Hilbert spaces and principal component analysis for functional extremes," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    8. Durieu, Olivier & Wang, Yizao, 2022. "Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 55-88.

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