IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1607.04739.html
   My bibliography  Save this paper

Multiple risk factor dependence structures: Distributional properties

Author

Listed:
  • Jianxi Su
  • Edward Furman

Abstract

We introduce a class of dependence structures, that we call the Multiple Risk Factor (MRF) dependence structures. On the one hand, the new constructions extend the popular CreditRisk+ approach, and as such they formally describe default risk portfolios exposed to an arbitrary number of fatal risk factors with conditionally exponential and dependent hitting (or occurrence) times. On the other hand, the MRF structures can be seen as an encompassing family of multivariate probability distributions with univariate margins distributed Pareto of the 2nd kind, and in this role they can be used to model insurance risk portfolios of dependent and heavy tailed risk components.

Suggested Citation

  • Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Distributional properties," Papers 1607.04739, arXiv.org.
    • Handle: RePEc:arx:papers:1607.04739
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1607.04739
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
    2. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    3. Raluca Vernic, 2011. "Tail Conditional Expectation for the Multivariate Pareto Distribution of the Second Kind: Another Approach," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 121-137, March.
    4. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    5. John Geweke & Gianni Amisano, 2011. "Hierarchical Markov normal mixture models with applications to financial asset returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 1-29, January/F.
    6. Bernd Engelmann & Robert Rauhmeier (ed.), 2011. "The Basel II Risk Parameters," Springer Books, Springer, number 978-3-642-16114-8, September.
    7. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    8. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    9. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
    10. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    11. Furman, Edward & Landsman, Zinoviy, 2005. "Risk capital decomposition for a multivariate dependent gamma portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 635-649, December.
    12. Jianxi Su & Edward Furman, 2016. "A form of multivariate Pareto distribution with applications to financial risk measurement," Papers 1607.04737, arXiv.org.
    13. Chiragiev, Arthur & Landsman, Zinoviy, 2009. "Multivariate flexible Pareto model: Dependency structure, properties and characterizations," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1733-1743, August.
    14. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
    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. Jevtić, P. & Hurd, T.R., 2017. "The joint mortality of couples in continuous time," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 90-97.
    2. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Copulas and related properties," Papers 1610.02126, arXiv.org.
    3. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Copulas and related properties," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 109-121.

    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. Jianxi Su & Edward Furman, 2016. "A form of multivariate Pareto distribution with applications to financial risk measurement," Papers 1607.04737, arXiv.org.
    2. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Distributional properties," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 56-68.
    3. Furman, Edward & Kye, Yisub & Su, Jianxi, 2021. "Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 153-167.
    4. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    5. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    6. Mohammed, Nawaf & Furman, Edward & Su, Jianxi, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 425-436.
    7. Furman, Edward & Hackmann, Daniel & Kuznetsov, Alexey, 2020. "On log-normal convolutions: An analytical–numerical method with applications to economic capital determination," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 120-134.
    8. Nadezhda Gribkova & Ričardas Zitikis, 2019. "Weighted allocations, their concomitant-based estimators, and asymptotics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 811-835, August.
    9. Alexandru V. Asimit & Raluca Vernic & Riċardas Zitikis, 2013. "Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model," Risks, MDPI, vol. 1(1), pages 1-20, March.
    10. Nawaf Mohammed & Edward Furman & Jianxi Su, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of Conditional Tail Expectation," Papers 2102.05003, arXiv.org, revised Aug 2021.
    11. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
    12. Brahimi, Brahim & Meraghni, Djamel & Necir, Abdelhakim & Zitikis, Ričardas, 2011. "Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 325-334.
    13. Furman, Edward & Kuznetsov, Alexey & Zitikis, Ričardas, 2018. "Weighted risk capital allocations in the presence of systematic risk," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 75-81.
    14. Denuit, Michel, 2019. "Size-biased transform and conditional mean risk sharing, with application to P2P insurance and tontines," LIDAM Discussion Papers ISBA 2019010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Denuit, Michel & Robert, Christian Y., 2020. "Conditional tail expectation decomposition and conditional mean risk sharing for dependent and conditionally independent risks," LIDAM Discussion Papers ISBA 2020018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.
    17. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Copulas and related properties," Papers 1610.02126, arXiv.org.
    18. Denuit, Michel, 2019. "Size-biased risk measures of compound sums," LIDAM Discussion Papers ISBA 2019009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Li, Xiaohu & Lin, Jianhua, 2011. "Stochastic orders in time transformed exponential models with applications," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 47-52, July.
    20. Eric C. K. Cheung & Oscar Peralta & Jae-Kyung Woo, 2021. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Papers 2201.11122, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1607.04739. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.
    pFad - Phonifier reborn

    Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

    Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


    Alternative Proxies:

    Alternative Proxy

    pFad Proxy

    pFad v3 Proxy

    pFad v4 Proxy