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An application of comonotonicity theory in a stochastic life annuity framework

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  • Liu, Xiaoming
  • Jang, Jisoo
  • Mee Kim, Sun

Abstract

A life annuity contract is an insurance instrument which pays pre-scheduled living benefits conditional on the survival of the annuitant. In order to manage the risk borne by annuity providers, one needs to take into account all sources of uncertainty that affect the value of future obligations under the contract. In this paper, we define the concept of annuity rate as the conditional expected present value random variable of future payments of the annuity, given the future dynamics of its risk factors. The annuity rate deals with the non-diversifiable systematic risk contained in the life annuity contract, and it involves mortality risk as well as investment risk. While it is plausible to assume that there is no correlation between the two risks, each affects the annuity rate through a combination of dependent random variables. In order to understand the probabilistic profile of the annuity rate, we apply comonotonicity theory to approximate its quantile function. We also derive accurate upper and lower bounds for prediction intervals for annuity rates. We use the Lee-Carter model for mortality risk and the Vasicek model for the term structure of interest rates with an annually renewable fixed-income investment policy. Different investment strategies can be handled using this framework.

Suggested Citation

  • Liu, Xiaoming & Jang, Jisoo & Mee Kim, Sun, 2011. "An application of comonotonicity theory in a stochastic life annuity framework," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 271-279, March.
    • Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:271-279
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    References listed on IDEAS

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    1. Denuit, Michel, 2008. "Comonotonic approximations to quantiles of life annuity conditional expected present value," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 831-838, April.
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    3. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    4. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    5. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    6. Hoedemakers, Tom & Darkiewicz, Grzegorz & Goovaerts, Marc, 2005. "Approximations for life annuity contracts in a stochastic financial environment," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 239-269, October.
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    Cited by:

    1. Zhao, Yixing & Mamon, Rogemar, 2018. "An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 1-12.

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