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Credibility Methods for Individual Life Insurance

Author

Listed:
  • Yikai (Maxwell) Gong

    (BlueCrest Capital, New York, NY 10022, USA)

  • Zhuangdi Li

    (PayPal, Inc., San Jose, CA 95131, USA)

  • Maria Milazzo

    (Unum, Chattanooga, TN 37402, USA)

  • Kristen Moore

    (Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA)

  • Matthew Provencher

    (Mutual of Omaha Insurance Co., Omaha, NE 68175-1004, USA)

Abstract

Credibility theory is used widely in group health and casualty insurance. However, it is generally not used in individual life and annuity business. With the introduction of principle-based reserving (PBR), which relies more heavily on company-specific experience, credibility theory is becoming increasingly important for life actuaries. In this paper, we review the two most commonly used credibility methods: limited fluctuation and greatest accuracy (Bühlmann) credibility. We apply the limited fluctuation method to M Financial Group’s experience data and describe some general qualitative observations. In addition, we use simulation to generate a universe of data and compute Limited Fluctuation and greatest accuracy credibility factors for actual-to-expected (A/E) mortality ratios. We also compare the two credibility factors to an intuitive benchmark credibility measure. We see that for our simulated data set, the limited fluctuation factors are significantly lower than the greatest accuracy factors, particularly for low numbers of claims. Thus, the limited fluctuation method may understate the credibility for companies with favorable mortality experience. The greatest accuracy method has a stronger mathematical foundation, but it generally cannot be applied in practice because of data constraints. The National Association of Insurance Commissioners (NAIC) recognizes and is addressing the need for life insurance experience data in support of PBR—this is an area of current work.

Suggested Citation

  • Yikai (Maxwell) Gong & Zhuangdi Li & Maria Milazzo & Kristen Moore & Matthew Provencher, 2018. "Credibility Methods for Individual Life Insurance," Risks, MDPI, vol. 6(4), pages 1-16, December.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:4:p:144-:d:189754
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    References listed on IDEAS

    as
    1. Nelder, J.A. & Verrall, R.J., 1997. "Credibility Theory and Generalized Linear Models," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 71-82, May.
    2. 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.
    3. Christiansen, Marcus C. & Schinzinger, Edo, 2016. "A Credibility Approach For Combining Likelihoods Of Generalized Linear Models," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 531-569, September.
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    Cited by:

    1. Apostolos Bozikas & Georgios Pitselis, 2019. "Credible Regression Approaches to Forecast Mortality for Populations with Limited Data," Risks, MDPI, vol. 7(1), pages 1-22, February.

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