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Estimating Copula-Based Extension of Tail Value-at-Risk and Its Application in Insurance Claim

Author

Listed:
  • Khreshna Syuhada

    (Statistics Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia)

  • Oki Neswan

    (Analysis and Geometry Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia)

  • Bony Parulian Josaphat

    (Statistics Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia)

Abstract

Dependent Tail Value-at-Risk, abbreviated as DTVaR, is a copula-based extension of Tail Value-at-Risk (TVaR). This risk measure is an expectation of a target loss once the loss and its associated loss are above their respective quantiles but bounded above by their respective larger quantiles. In this paper, we propose nonparametric estimators for DTVaR and establish their property of consistency. Moreover, we also propose the variability measure around this expected value truncated by the quantiles, called the Dependent Conditional Tail Variance (DCTV). We use this measure for constructing confidence intervals of the DTVaR. Both parametric and nonparametric approaches for DTVaR estimations are explored. Furthermore, we assess the performance of DTVaR estimations using a proposed backtest based on the DCTV. As for the numerical study, we take an application in the insurance claim amount.

Suggested Citation

  • Khreshna Syuhada & Oki Neswan & Bony Parulian Josaphat, 2022. "Estimating Copula-Based Extension of Tail Value-at-Risk and Its Application in Insurance Claim," Risks, MDPI, vol. 10(6), pages 1-26, May.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:6:p:113-:d:827698
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    References listed on IDEAS

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    1. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2015. "A comparison of Expected Shortfall estimation models," Journal of Economics and Business, Elsevier, vol. 78(C), pages 14-47.
    2. Roba Bairakdar & Lu Cao & Melina Mailhot, 2020. "Range Value-at-Risk: Multivariate and Extreme Values," Papers 2005.12473, arXiv.org.
    3. Jonathan El Methni & Laurent Gardes & Stéphane Girard, 2014. "Non-parametric Estimation of Extreme Risk Measures from Conditional Heavy-tailed Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 988-1012, December.
    4. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    5. Wang, Ruodu & Wei, Yunran, 2020. "Characterizing optimal allocations in quantile-based risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 288-300.
    6. Heuchenne, Cedric & Laurent, Geraldine, 2014. "Parametric conditional variance estimation in location-scale models with censored data," LIDAM Discussion Papers ISBA 2014051, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

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    2. Jinyu Zhou & Jigao Yan & Dongya Cheng, 2024. "Strong consistency of tail value-at-risk estimator and corresponding general results under widely orthant dependent samples," Statistical Papers, Springer, vol. 65(6), pages 3357-3394, August.

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