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Pure robust versus robust portfolio unbiased—Credibility and asymptotic optimality

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  • Pitselis, Georgios

Abstract

Empirical credibility estimation, which is a credibility counterpart of empirical Bayes estimation, lacks robustness due to the sensitivity of estimators to outlier events. In this paper we combine robust statistics with empirical linear Bayes estimation and derive robust asymptotic optimality based on Norberg’s (1980) proposal. Robust portfolio-unbiased empirical regression credibility is derived and its asymptotic optimality is proved, under not very restrictive assumptions. The asymptotic optimality of pure robust credibility estimators is also proved. The superiority of the pure robust credibility estimation against the robust portfolio-unbiased credibility estimation is presented and verified with numerical results.

Suggested Citation

  • Pitselis, Georgios, 2013. "Pure robust versus robust portfolio unbiased—Credibility and asymptotic optimality," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 391-403.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:2:p:391-403
    DOI: 10.1016/j.insmatheco.2013.01.008
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    References listed on IDEAS

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    1. Landsman, Zinoviy & Makov, Udi E., 1999. "Credibility evaluation for the exponential dispersion family," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 23-29, March.
    2. repec:cup:astinb:v:20:y:1990:i:02:p:167-172_00 is not listed on IDEAS
    3. repec:cup:astinb:v:8:y:1974:i:01:p:77-90_00 is not listed on IDEAS
    4. Landsman, Zinoviy, 2002. "Credibility theory: a new view from the theory of second order optimal statistics," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 351-362, June.
    5. repec:cup:astinb:v:23:y:1993:i:01:p:117-143_00 is not listed on IDEAS
    6. repec:cup:astinb:v:10:y:1978:i:01:p:99-112_00 is not listed on IDEAS
    7. Pitselis, Georgios, 2008. "Robust regression credibility: The influence function approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 288-300, February.
    8. Mashayekhi, Mostafa, 2002. "On asymptotic optimality in empirical Bayes credibility," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 285-295, October.
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    Cited by:

    1. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2022. "Satisficing credibility for heterogeneous risks," European Journal of Operational Research, Elsevier, vol. 298(2), pages 752-768.

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