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Quantile Credibility Models with Common Effects

Author

Listed:
  • Wei Wang

    (Department of Financial Engineering, Ningbo University, Ningbo 315211, China)

  • Limin Wen

    (School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022, China)

  • Zhixin Yang

    (Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA)

  • Quan Yuan

    (Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA)

Abstract

Different from classical Bühlmann and Bühlmann Straub credibility models in which independence between different risks are assumed, this paper takes dependence between risks into consideration and extends the classical Bühlmann model by introducing a common stochastic shock element. What is more, instead of relying on complete information of historical data, we aim to derive the premium using quantile of the available data. By the method of linear regression, we manage to obtain the quantile credibility premium with common effects. Our result is the generalization of existing results in credibility theory. Both quantile credibility model proposed by Pitselis (2013) and credibility premium for models with dependence induced by common effects obtained by Wen et al. (2009) are special cases of our model. Numerical simulations are also presented to illustrate the impact of quantile credibility with common effect.

Suggested Citation

  • Wei Wang & Limin Wen & Zhixin Yang & Quan Yuan, 2020. "Quantile Credibility Models with Common Effects," Risks, MDPI, vol. 8(4), pages 1-10, September.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:4:p:100-:d:419448
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    References listed on IDEAS

    as
    1. Pitselis, Georgios, 2017. "Risk measures in a quantile regression credibility framework with Fama/French data applications," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 122-134.
    2. Edward Frees & Virginia Young & Yu Luo, 2001. "Case Studies Using Panel Data Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(4), pages 24-42.
    3. Pitselis, Georgios, 2016. "Credible risk measures with applications in actuarial sciences and finance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 373-386.
    4. Tsai, Cary Chi-Liang & Wu, Adelaide Di, 2020. "Incorporating hierarchical credibility theory into modelling of multi-country mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 37-54.
    5. Kudryavtsev, Andrey A., 2009. "Using quantile regression for rate-making," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 296-304, October.
    6. Pitt, D. G. W., 2006. "Regression Quantile Analysis of Claim Termination Rates for Income Protection Insurance," Annals of Actuarial Science, Cambridge University Press, vol. 1(2), pages 345-357, September.
    7. Frees, Edward W. & Young, Virginia R. & Luo, Yu, 1999. "A longitudinal data analysis interpretation of credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 229-247, May.
    8. Bolance, Catalina & Guillen, Montserrat & Pinquet, Jean, 2003. "Time-varying credibility for frequency risk models: estimation and tests for autoregressive specifications on the random effects," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 273-282, October.
    9. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    10. Wen, Limin & Wu, Xianyi & Zhou, Xian, 2009. "The credibility premiums for models with dependence induced by common effects," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 19-25, February.
    11. Yeo, Keng Leong & Valdez, Emiliano A., 2006. "Claim dependence with common effects in credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 609-629, June.
    12. Wu, Xianyi & Zhou, Xian, 2006. "A new characterization of distortion premiums via countable additivity for comonotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 324-334, April.
    13. Purcaru, Oana & Denuit, Michel, 2003. "Dependence in Dynamic Claim Frequency Credibility Models," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 23-40, May.
    14. Bozikas, Apostolos & Pitselis, Georgios, 2020. "Incorporating crossed classification credibility into the Lee–Carter model for multi-population mortality data," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 353-368.
    15. Pitselis, Georgios, 2020. "Multi-stage nested classification credibility quantile regression model," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 162-176.
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