IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v9y2009i2p207-215.html
   My bibliography  Save this article

Law of large numbers and large deviations for dependent risks

Author

Listed:
  • Ramona Maier
  • Mario Wuthrich

Abstract

We analyse the mathematical structure of models for large risk portfolios, especially for credit risk models. These risk portfolios are modelled using a multivariate mixture model for the dependence structure between the risks. The dependence structures are characterized by latent variables Θ, which play the role of systematic risks. We show that, depending on the choice of the distribution of Θ, there are different asymptotic behaviours for the aggregated risk portfolio, namely law of large numbers/central limit theorem behaviour and large deviation behaviour.

Suggested Citation

  • Ramona Maier & Mario Wuthrich, 2009. "Law of large numbers and large deviations for dependent risks," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 207-215.
    • Handle: RePEc:taf:quantf:v:9:y:2009:i:2:p:207-215
    DOI: 10.1080/14697680801986587
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680801986587
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697680801986587?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. Niall Whelan, 2004. "Sampling from Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 339-352.
    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. Georg Ch. Pflug & Alois Pichler, 2018. "Systemic risk and copula models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(2), pages 465-483, June.

    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. Luca Riccetti, 2013. "A copula–GARCH model for macro asset allocation of a portfolio with commodities," Empirical Economics, Springer, vol. 44(3), pages 1315-1336, June.
    2. Okhrin Ostap & Okhrin Yarema & Schmid Wolfgang, 2013. "Properties of hierarchical Archimedean copulas," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 21-54, March.
    3. Choe, Geon Ho & Jang, Hyun Jin, 2011. "Efficient algorithms for basket default swap pricing with multivariate Archimedean copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 205-213, March.
    4. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 22(2), pages 98-134.
    5. Liu, X. & Xu, W. & Odening, M., 2011. "Lassen sich Ertragsrisiken in der Landwirtschaft global diversifizieren?," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 46, March.
    6. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    7. Weiß, Gregor N.F. & Scheffer, Marcus, 2015. "Mixture pair-copula-constructions," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 175-191.
    8. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    9. Dalla Valle, Luciana & De Giuli, Maria Elena & Tarantola, Claudia & Manelli, Claudio, 2016. "Default probability estimation via pair copula constructions," European Journal of Operational Research, Elsevier, vol. 249(1), pages 298-311.
    10. Olusola O. Ayantobo & Yi Li & Songbai Song, 2019. "Multivariate Drought Frequency Analysis using Four-Variate Symmetric and Asymmetric Archimedean Copula Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(1), pages 103-127, January.
    11. Weiß, Gregor N.F. & Supper, Hendrik, 2013. "Forecasting liquidity-adjusted intraday Value-at-Risk with vine copulas," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3334-3350.
    12. Ostap Okhrin & Martin Odening & Wei Xu, 2013. "Systemic Weather Risk and Crop Insurance: The Case of China," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(2), pages 351-372, June.
    13. repec:jss:jstsof:21:i04 is not listed on IDEAS
    14. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.
    15. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    16. Diakarya Barro & Moumouni Diallo & Remi Guillaume Bagré, 2016. "Spatial Tail Dependence and Survival Stability in a Class of Archimedean Copulas," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-8, July.
    17. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    18. Bee, Marco, 2011. "Adaptive Importance Sampling for simulating copula-based distributions," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 237-245, March.
    19. Zhou, Rui & Ji, Min, 2021. "Modelling mortality dependence: An application of dynamic vine copula," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 241-255.
    20. Calabrese, Raffaella & Degl’Innocenti, Marta & Osmetti, Silvia Angela, 2017. "The effectiveness of TARP-CPP on the US banking industry: A new copula-based approach," European Journal of Operational Research, Elsevier, vol. 256(3), pages 1029-1037.
    21. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2013. "On the structure and estimation of hierarchical Archimedean copulas," Journal of Econometrics, Elsevier, vol. 173(2), pages 189-204.

    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:taf:quantf:v:9:y:2009:i:2:p:207-215. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.