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**Hedging mortality/longevity risks for multiple years.**
*(English)*
Zbl 1437.91397

Summary: In this article, we develop strategies of hedging multiyear mortality (longevity) risk for a life insurer (an annuity provider) through purchasing some mortality-linked securities from a financial intermediary. Under the multiyear hedges for a life insurer (an annuity provider) involving two uncertain factors – the mortality rate and the number of life insureds (annuity recipients) – we derive closed-form formulas for the optimal units of purchasing underlying mortality-linked securities. Numerical illustrations show that the downside risk of loss because of mortality (longevity) risk for the life insurer (annuity provider) can be significantly hedged by purchasing the optimal units of mortality-linked securities, and the sample risk can be reduced by increasing the number of life insureds (annuity recipients) at issue. For a financial intermediary, adopting an optimal weight of a portfolio of life and annuity business can reduce extreme losses from the longevity risk but could slightly increase losses from the mortality risk, and the sample risk cannot necessarily be eliminated by increasing the number of life insureds/annuity recipients at issue.

### MSC:

91G05 | Actuarial mathematics |

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\textit{T. Lin} and \textit{C. C. L. Tsai}, N. Am. Actuar. J. 24, No. 1, 118--140 (2020; Zbl 1437.91397)

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