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Actuarial applications of the linear hazard transform in life contingencies

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  • Tsai, Cary Chi-Liang
  • Jiang, Lingzhi

Abstract

In this paper, we study the linear hazard transform and its applications in life contingencies. Under the linear hazard transform, the survival function of a risk is distorted, which provides a safety margin for pricing insurance products. Combining the assumption of [alpha]-power approximation with the linear hazard transform, the net single premium of a continuous life insurance policy can be approximated in terms of the net single premiums of discrete ones. Moreover, Macaulay duration, modified duration and dollar duration, all measuring the sensitivity of the price of a life insurance policy to force of mortality movements under the linear hazard transform, are defined and investigated. Some examples are given for illustration.

Suggested Citation

  • Tsai, Cary Chi-Liang & Jiang, Lingzhi, 2011. "Actuarial applications of the linear hazard transform in life contingencies," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 70-80, July.
    • Handle: RePEc:eee:insuma:v:49:y:2011:i:1:p:70-80
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    References listed on IDEAS

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    1. Jones, Bruce L. & Mereu, John A., 2000. "A family of fractional age assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 261-276, October.
    2. Dahan, Merav & Frostig, Esther & Langberg, Naftali A., 2003. "Analysis of heterogeneous endowment policies portfolios under fractional approximations," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 567-584, December.
    3. Wang, Shaun, 1996. "Ordering of risks under PH-transforms," Insurance: Mathematics and Economics, Elsevier, vol. 18(2), pages 109-114, July.
    4. Frostig, Esther, 2003. "Properties of the power family of fractional age approximations," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 163-171, August.
    5. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
    6. Esther Frostig, 2002. "Comparison Between Future Lifetime Distribution and Its Approximations," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(2), pages 11-17.
    7. Jones, Bruce L. & Mereu, John A., 2002. "A critique of fractional age assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 363-370, June.
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    Cited by:

    1. Lin, Tzuling & Tsai, Cary Chi-Liang, 2013. "On the mortality/longevity risk hedging with mortality immunization," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 580-596.
    2. Zhou, Kenneth Q. & Li, Johnny Siu-Hang, 2019. "Delta-hedging longevity risk under the M7–M5 model: The impact of cohort effect uncertainty and population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 1-21.
    3. Tsai, Cary Chi-Liang & Chung, San-Lin, 2013. "Actuarial applications of the linear hazard transform in mortality immunization," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 48-63.

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