IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2221-d462015.html
   My bibliography  Save this article

Adaptive Bernstein Copulas and Risk Management

Author

Listed:
  • Dietmar Pfeifer

    (Institute of Mathematics, Carl von Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany)

  • Olena Ragulina

    (Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Str. 64, 01601 Kyiv, Ukraine)

Abstract

We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we compare different approaches of Bernstein and Gaussian copulas regarding the estimation of risk measures in risk management.

Suggested Citation

  • Dietmar Pfeifer & Olena Ragulina, 2020. "Adaptive Bernstein Copulas and Risk Management," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2221-:d:462015
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2221/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2221/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhong Guan, 2017. "Bernstein polynomial model for grouped continuous data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 831-848, October.
    2. Junker, Robert R. & Griessenberger, Florian & Trutschnig, Wolfgang, 2021. "Estimating scale-invariant directed dependence of bivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    3. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2017. "The empirical beta copula," LIDAM Reprints ISBA 2017005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    5. Berghaus, Betina & Segers, Johan, 2017. "Weak convergence of the weighted empirical beta copula process," LIDAM Discussion Papers ISBA 2017015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Dietmar Pfeifer & Olena Ragulina, 2018. "Generating VaR Scenarios under Solvency II with Product Beta Distributions," Risks, MDPI, vol. 6(4), pages 1-15, October.
    7. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2017. "The empirical beta copula," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 35-51.
    8. Zhong Guan, 2016. "Efficient and robust density estimation using Bernstein type polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 250-271, June.
    9. Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
    10. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    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. Donghun Lee, 2022. "Knowledge Gradient: Capturing Value of Information in Iterative Decisions under Uncertainty," Mathematics, MDPI, vol. 10(23), pages 1-20, November.

    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. Dietmar Pfeifer & Olena Ragulina, 2020. "Adaptive Bernstein Copulas and Risk Management," Papers 2011.00909, arXiv.org, revised Mar 2021.
    2. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    3. Eddie Anderson & Artem Prokhorov & Yajing Zhu, 2020. "A Simple Estimator of Two‐Dimensional Copulas, with Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1375-1412, December.
    4. Junker, Robert R. & Griessenberger, Florian & Trutschnig, Wolfgang, 2021. "Estimating scale-invariant directed dependence of bivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    5. Hofert, Marius & Prasad, Avinash & Zhu, Mu, 2022. "Multivariate time-series modeling with generative neural networks," Econometrics and Statistics, Elsevier, vol. 23(C), pages 147-164.
    6. Kiriliouk, Anna & Segers, Johan & Tafakori, Laleh, 2018. "An estimator of the stable tail dependence function based on the empirical beta copula," LIDAM Discussion Papers ISBA 2018029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Lu Lu & Sujit Ghosh, 2023. "Nonparametric Estimation of Multivariate Copula Using Empirical Bayes Methods," Mathematics, MDPI, vol. 11(20), pages 1-22, October.
    8. Kiriliouk, Anna & Segers, Johan & Tafakori, Laleh, 2017. "An estimator of the stable tail dependence function based on the empirical beta copula," LIDAM Discussion Papers ISBA 2017028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Berghaus, Betina & Segers, Johan, 2017. "Weak convergence of the weighted empirical beta copula process," LIDAM Discussion Papers ISBA 2017015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Shih, Jia-Han & Emura, Takeshi, 2021. "On the copula correlation ratio and its generalization," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    11. Laverny, Oskar & Masiello, Esterina & Maume-Deschamps, Véronique & Rullière, Didier, 2021. "Dependence structure estimation using Copula Recursive Trees," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    12. Kiriliouk, Anna, 2020. "Hypothesis testing for tail dependence parameters on the boundary of the parameter space," Econometrics and Statistics, Elsevier, vol. 16(C), pages 121-135.
    13. Frédéric Ouimet, 2021. "General Formulas for the Central and Non-Central Moments of the Multinomial Distribution," Stats, MDPI, vol. 4(1), pages 1-10, January.
    14. Aleksy Leeuwenkamp & Wentao Hu, 2023. "New general dependence measures: construction, estimation and application to high-frequency stock returns," Papers 2309.00025, arXiv.org.
    15. Berghaus, Betina & Segers, Johan, 2018. "Weak convergence of the weighted empirical beta copula process," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 266-281.
    16. Ćmiel, Bogdan & Ledwina, Teresa, 2020. "Validation of association," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 55-67.
    17. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2022. "Stochastic representation of FGM copulas using multivariate Bernoulli random variables," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    18. Kojadinovic, Ivan & Stemikovskaya, Kristina, 2019. "Subsampling (weighted smooth) empirical copula processes," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 704-723.
    19. Dongliang Wang & Xueya Cai, 2021. "Smooth ROC curve estimation via Bernstein polynomials," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-12, May.
    20. Kiriliouk, Anna & Segers, Johan & Tsukahara, Hideatsu, 2019. "On Some Resampling Procedures with the Empirical Beta Copula," LIDAM Discussion Papers ISBA 2019012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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:gam:jmathe:v:8:y:2020:i:12:p:2221-:d:462015. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.