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Copula based hierarchical risk aggregation through sample reordering

Author

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  • Arbenz, Philipp
  • Hummel, Christoph
  • Mainik, Georg

Abstract

For high-dimensional risk aggregation purposes, most popular copula classes are too restrictive in terms of attainable dependence structures. These limitations aggravate with increasing dimension. We study a hierarchical risk aggregation method which is flexible in high dimensions. With this method it suffices to specify a low dimensional copula for each aggregation step in the hierarchy. Copulas and margins of arbitrary kind can be combined. We give an algorithm for numerical approximation which introduces dependence between originally independent marginal samples through reordering.

Suggested Citation

  • Arbenz, Philipp & Hummel, Christoph & Mainik, Georg, 2012. "Copula based hierarchical risk aggregation through sample reordering," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 122-133.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:122-133
    DOI: 10.1016/j.insmatheco.2012.03.009
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    References listed on IDEAS

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    Cited by:

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    2. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    3. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
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    6. Andreas Tsanakas & Pietro Millossovich, 2016. "Sensitivity Analysis Using Risk Measures," Risk Analysis, John Wiley & Sons, vol. 36(1), pages 30-48, January.
    7. Souhaib Ben Taieb & James W. Taylor & Rob J. Hyndman, 2017. "Coherent Probabilistic Forecasts for Hierarchical Time Series," Monash Econometrics and Business Statistics Working Papers 3/17, Monash University, Department of Econometrics and Business Statistics.
    8. Mejdoub, Hanène & Ben Arab, Mounira, 2018. "Impact of dependence modeling of non-life insurance risks on capital requirement: D-Vine Copula approach," Research in International Business and Finance, Elsevier, vol. 45(C), pages 208-218.
    9. Mainik, Georg, 2015. "Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 197-216.
    10. Lee, Chien-Chiang & Chang, Chi-Hung & Chen, Mei-Ping, 2015. "Industry co-movements of American depository receipts: Evidences from the copula approaches," Economic Modelling, Elsevier, vol. 46(C), pages 301-314.
    11. Rafał Wójcik & Charlie Wusuo Liu & Jayanta Guin, 2019. "Direct and Hierarchical Models for Aggregating Spatially Dependent Catastrophe Risks," Risks, MDPI, vol. 7(2), pages 1-22, May.
    12. Dietmar Pfeifer & Olena Ragulina, 2020. "Generating unfavourable VaR scenarios with patchwork copulas," Papers 2011.06281, arXiv.org, revised May 2021.
    13. Zaks, Yaniv & Tsanakas, Andreas, 2014. "Optimal capital allocation in a hierarchical corporate structure," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 48-55.
    14. Pfeifer Dietmar & Ragulina Olena, 2021. "Generating unfavourable VaR scenarios under Solvency II with patchwork copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 327-346, January.
    15. Baltuttis, Dennik & Töppel, Jannick & Tränkler, Timm & Wiethe, Christian, 2020. "Managing the risks of energy efficiency insurances in a portfolio context: An actuarial diversification approach," International Review of Financial Analysis, Elsevier, vol. 68(C).
    16. Joe, Harry & Sang, Peijun, 2016. "Multivariate models for dependent clusters of variables with conditional independence given aggregation variables," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 114-132.
    17. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 273-280.
    18. Rafał Wójcik & Charlie Wusuo Liu, 2022. "Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks," Risks, MDPI, vol. 10(8), pages 1-24, July.
    19. Georg Mainik, 2015. "Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions," Papers 1508.02749, arXiv.org.
    20. Bernardi, Enrico & Falangi, Federico & Romagnoli, Silvia, 2015. "A hierarchical copula-based world-wide valuation of sovereign risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 155-169.

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    More about this item

    Keywords

    IM12; IM22; IM43; IE43; IE46; Hierarchical risk aggregation; Copulas; High-dimensional dependence; Iman–Conover method;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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