IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v429y2022ics0096300322002880.html
   My bibliography  Save this article

Extreme generators of shock induced copulas

Author

Listed:
  • Kokol Bukovšek, Damjana
  • Košir, Tomaž
  • Mojškerc, Blaž
  • Omladič, Matjaž

Abstract

In a recent paper, extreme points (in the Krein-Milman sense) of the class of semilinear copulas were introduced, motivated by the lack of known extreme copulas such as shuffles of M. We propose an extension of this concept to the class of all bivariate shock induced copulas, the most well-known part of them being the Marshall-Olkin copulas. This class properly contains semilinear copulas. Our technique coincides with the existing notion on them and has some advantages. First, it is defined on a wider family of copulas, which is helpful in finding more examples of extreme copulas. Second, we show that they are dense in each class they belong to (including the class of semilinear copulas) in a stronger sense than in the Krein-Milman approach; actually, they are dense in a similar way as shuffles of M are dense in the set of all copulas. Third, this definition enables practitioners to give stochastic interpretation of extremality. Roughly speaking, a shock induced copula is extreme whenever the inducing shocks have pairwise disjoint supports.

Suggested Citation

  • Kokol Bukovšek, Damjana & Košir, Tomaž & Mojškerc, Blaž & Omladič, Matjaž, 2022. "Extreme generators of shock induced copulas," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    • Handle: RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322002880
    DOI: 10.1016/j.amc.2022.127214
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322002880
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127214?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. Lindskog, Filip & McNeil, Alexander J., 2003. "Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 209-238, November.
    2. Durante, Fabrizio & Fernández Sánchez, Juan & Trutschnig, Wolfgang, 2014. "Multivariate copulas with hairpin support," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 323-334.
    3. Montes, Ignacio & Miranda, Enrique & Montes, Susana, 2014. "Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance," European Journal of Operational Research, Elsevier, vol. 234(1), pages 209-220.
    4. Sabrina Mulinacci, 2018. "Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 205-236, March.
    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. Tariq Saali & Mhamed Mesfioui & Ani Shabri, 2023. "Multivariate Extension of Raftery Copula," Mathematics, MDPI, vol. 11(2), pages 1-15, January.

    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. Sabrina Mulinacci, 2022. "A Marshall-Olkin Type Multivariate Model with Underlying Dependent Shocks," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2455-2484, December.
    2. Damjana Kokol Bukovv{s}ek & Tomav{z} Kov{s}ir & Blav{z} Mojv{s}kerc & Matjav{z} Omladiv{c}, 2018. "Asymmetric linkages: maxmin vs. reflected maxmin copulas," Papers 1808.07737, arXiv.org, revised Jul 2019.
    3. Jiang, Yanping & Liang, Xia & Liang, Haiming & Yang, Ningman, 2018. "Multiple criteria decision making with interval stochastic variables: A method based on interval stochastic dominance," European Journal of Operational Research, Elsevier, vol. 271(2), pages 632-643.
    4. Tomasz R. Bielecki & Areski Cousin & Stéphane Crépey & Alexander Herbertsson, 2014. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 90-102, April.
    5. Thomas Deschatre & Xavier Warin, 2023. "A Common Shock Model for multidimensional electricity intraday price modelling with application to battery valuation," Papers 2307.16619, arXiv.org.
    6. Christian Hering & Jan-Frederik Mai, 2012. "Moment-based estimation of extendible Marshall-Olkin copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 601-620, July.
    7. Robert Jarrow & Jeff Oxman & Yildiray Yildirim, 2010. "The cost of operational risk loss insurance," Review of Derivatives Research, Springer, vol. 13(3), pages 273-295, October.
    8. H. Klammler & P. S. C. Rao & K. Hatfield, 2018. "Modeling dynamic resilience in coupled technological-social systems subjected to stochastic disturbance regimes," Environment Systems and Decisions, Springer, vol. 38(1), pages 140-159, March.
    9. Liu, Wenyue & Cadenillas, Abel, 2023. "Optimal insurance contracts for a shot-noise Cox claim process and persistent insured's actions," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 69-93.
    10. Levy, Moshe, 2022. "An inter-temporal CAPM based on First order Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 298(2), pages 734-739.
    11. Mittnik, Stefan & Yener, Tina, 2008. "Value-at-Risk and expected shortfall for rare events," CFS Working Paper Series 2008/14, Center for Financial Studies (CFS).
    12. Yinghui Dong & Kam C. Yuen & Guojing Wang & Chongfeng Wu, 2016. "A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 459-486, June.
    13. Balakrishna, B S, 2010. "Levy Subordinator Model: A Two Parameter Model of Default Dependency," MPRA Paper 26274, University Library of Munich, Germany.
    14. Bielecki, Tomasz R. & Cousin, Areski & Crépey, Stéphane & Herbertsson, Alexander, 2011. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model (Previous title: Dynamic Modeling of Portfolio Credit Risk with Common Shocks)," Working Papers in Economics 502, University of Gothenburg, Department of Economics, revised 12 Oct 2012.
    15. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Gamma Related Ornstein-Uhlenbeck Processes and their Simulation," Papers 2003.08810, arXiv.org.
    16. Bäuerle, Nicole & Blatter, Anja, 2011. "Optimal control and dependence modeling of insurance portfolios with Lévy dynamics," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 398-405, May.
    17. Beer, Simone & Braun, Alexander & Marugg, Andrin, 2019. "Pricing industry loss warranties in a Lévy–Frailty framework," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 171-181.
    18. Damiano Brigo & Cristin Buescu & Massimo Morini, 2011. "Impact of the first to default time on Bilateral CVA," Papers 1106.3496, arXiv.org.
    19. Matthias Scherer & Henrik Sloot, 2019. "Exogenous shock models: analytical characterization and probabilistic construction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 931-959, November.
    20. Xiang Hu & Lianzeng Zhang, 2016. "Ruin Probability in a Correlated Aggregate Claims Model with Common Poisson Shocks: Application to Reinsurance," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 675-689, September.

    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:apmaco:v:429:y:2022:i:c:s0096300322002880. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.