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Actuarial applications of the linear hazard transform in life contingencies

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  • Tsai, Cary Chi-Liang
  • Jiang, Lingzhi
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 49 (2011)
    Issue (Month): 1 (July)
    Pages: 70-80

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    Handle: RePEc:eee:insuma:v:49:y:2011:i:1:p:70-80

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: [alpha]-power approximation Fractional age assumptions Proportional hazard transform Linear hazard transform Macaulay duration Modified duration Dollar duration;

    References

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    1. Jones, Bruce L. & Mereu, John A., 2002. "A critique of fractional age assumptions," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 30(3), pages 363-370, June.
    2. Frostig, Esther, 2003. "Properties of the power family of fractional age approximations," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 33(1), pages 163-171, August.
    3. Dahan, Merav & Frostig, Esther & Langberg, Naftali A., 2003. "Analysis of heterogeneous endowment policies portfolios under fractional approximations," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 33(3), pages 567-584, December.
    4. Wang, Shaun, 1996. "Ordering of risks under PH-transforms," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 18(2), pages 109-114, July.
    5. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 17(1), pages 43-54, August.
    6. Jones, Bruce L. & Mereu, John A., 2000. "A family of fractional age assumptions," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 27(2), pages 261-276, October.
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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, Elsevier, vol. 53(3), pages 580-596.
    2. Tsai, Cary Chi-Liang & Chung, San-Lin, 2013. "Actuarial applications of the linear hazard transform in mortality immunization," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 53(1), pages 48-63.

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