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Actuarial applications of the linear hazard transform in mortality immunization

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  • Tsai, Cary Chi-Liang
  • Chung, San-Lin

Abstract

In this paper, we apply the linear hazard transform to mortality immunization. When there is a change in mortality rates, the respective surplus (negative reserve) changes for life insurance and annuity policies lead to oppositive sign changes, which provides mortality hedging strategies with a portfolio of life insurance and annuity policies. We first show that by the strategy of matching duration of the weighted surplus at time 0, the surplus changes at time 0 for both portfolios PTP (the n-year term life insurance and the n-year pure endowment) and PWA (the n-payment whole life insurance and the n-year deferred whole life annuity) in response to a proportional or parallel shift in the underlying force of mortality are always negative. Next, we prove that the term life insurance, the whole life insurance and the deferred whole life annuity cannot always form a feasible portfolio (feasibility means that all the weights of the product members of a portfolio are positive) by the strategy of matching two durations or one duration and one convexity of the weighted surplus at time 0. Finally, numerical examples including figures and tables are exhibited for illustrations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:48-63
    DOI: 10.1016/j.insmatheco.2013.03.013
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    References listed on IDEAS

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    1. Shiu, Elias S. W., 1988. "Immunization of multiple liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 7(4), pages 219-224, December.
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    Cited by:

    1. Cláudia Simões & Luís Oliveira & Jorge M. Bravo, 2021. "Immunization Strategies for Funding Multiple Inflation-Linked Retirement Income Benefits," Risks, MDPI, vol. 9(4), pages 1-28, March.
    2. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    3. 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.
    4. Lin, Tzuling & Wang, Chou-Wen & Tsai, Cary Chi-Liang, 2015. "Age-specific copula-AR-GARCH mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 110-124.
    5. 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.
    6. Changyu Liu & Michael Sherris, 2017. "Immunization and Hedging of Post Retirement Income Annuity Products," Risks, MDPI, vol. 5(1), pages 1-29, March.
    7. Tzuling Lin & Cary Chi‐Liang Tsai, 2023. "A new option for mortality–interest rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(2), pages 273-293, February.

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