IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v126y2016i9p2835-2859.html
   My bibliography  Save this article

Max-stable random sup-measures with comonotonic tail dependence

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414916000600
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2016.03.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. 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.
    3. Ressel, Paul, 2013. "Homogeneous distributions—And a spectral representation of classical mean values and stable tail dependence functions," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 246-256.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    3. 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.
    4. Stoev, Stilian & Wang, Yizao, 2019. "Exchangeable random partitions from max-infinitely-divisible distributions," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 50-56.
    5. 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.
    6. Hashorva Enkelejd, 2016. "Domination of sample maxima and related extremal dependence measures," Dependence Modeling, De Gruyter, vol. 6(1), pages 88-101, May.
    7. Rønn-Nielsen, Anders & Stehr, Mads, 2022. "Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 19-49.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Einmahl, John & Segers, Johan, 2020. "Empirical Tail Copulas for Functional Data," Other publications TiSEM edc722e6-cc70-4221-87a2-8, Tilburg University, School of Economics and Management.
    2. Marcon, Giulia & Padoan, Simone & Naveau, Philippe & Muliere, Pietro & Segers, Johan, 2016. "Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials," LIDAM Discussion Papers ISBA 2016020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Ressel Paul, 2019. "Copulas, stable tail dependence functions, and multivariate monotonicity," Dependence Modeling, De Gruyter, vol. 7(1), pages 247-258, January.
    4. Ressel Paul, 2018. "A multivariate version of Williamson’s theorem, ℓ1-symmetric survival functions, and generalized Archimedean copulas," Dependence Modeling, De Gruyter, vol. 6(1), pages 356-368, December.
    5. Campi, Luciano & Zabaljauregui, Diego, 2020. "Optimal market making under partial information with general intensities," LSE Research Online Documents on Economics 104612, London School of Economics and Political Science, LSE Library.
    6. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.
    7. Andrea Attar & Thomas Mariotti & François Salanié, 2021. "Entry-Proofness and Discriminatory Pricing under Adverse Selection," American Economic Review, American Economic Association, vol. 111(8), pages 2623-2659, August.
    8. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    9. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    10. He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
    11. Duggan, John, 2011. "General conditions for the existence of maximal elements via the uncovered set," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 755-759.
    12. Eduardo Perez & Delphine Prady, 2012. "Complicating to Persuade?," Working Papers hal-03583827, HAL.
    13. Romain Blanchard & Laurence Carassus & Miklós Rásonyi, 2018. "No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 241-281, October.
    14. René Aïd & Matteo Basei & Giorgia Callegaro & Luciano Campi & Tiziano Vargiolu, 2020. "Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 205-232, February.
    15. He, Wei & Yannelis, Nicholas C., 2015. "Equilibrium theory under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 86-95.
    16. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    17. Massimiliano Amarante & Mario Ghossoub & Edmund Phelps, 2012. "Contracting for Innovation under Knightian Uncertainty," Cahiers de recherche 18-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    18. Jeongwoo Lee & Jaeok Park, 2019. "Preemptive Entry in Sequential Auctions with Participation Cost," Working papers 2019rwp-141, Yonsei University, Yonsei Economics Research Institute.
    19. Sudhir A. Shah, 2016. "The Generalized Arrow-Pratt Coefficient," Working Papers id:10795, eSocialSciences.
    20. Luçon, Eric, 2020. "Quenched asymptotics for interacting diffusions on inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6783-6842.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:126:y:2016:i:9:p:2835-2859. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.