# Periodic or generational actuarial tables: which one to choose?

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## Abstract

The increase in life expectancy over the past several decades has been impressive and represents a key challenge for institutions that provide life insurance products. Indeed, when a new actuarial table is released with updated survival and death rates, such institutions need to update the amount of mathematical reserve that they need to set aside to guarantee the future payments of their annuities. As mortality forecasting techniques are currently well developed, it is relatively easy to forecast mortality over several decades and to directly use these forecast rates in the determination of the mathematical reserve needed to guarantee annuity payments. Future mortality evolution is then directly incorporated into the liabilities valuation of an institution, and it is thus commonly believed that such liabilities should not require much updating when a new actuarial table is released. In this paper, we demonstrate that contrary to this common belief, institutions that use generational tables (namely, tables including future mortality evolution) will most likely need to make more important adjustments (positive or negative) to their liabilities than will institutions using periodic (static) tables whenever a new table is released. By using three very different models to project mortality, we demonstrate that our findings are inherent in the required long horizons of the forecasts needed in the generational approach, with the uncertainty surrounding the forecast values increasing with the horizon. Therefore, generational tables may introduce more instability in a pension institution’s accounts than periodic tables.

## Keywords

Mortality rates Periodic actuarial tables Generational actuarial tables Life expectancy Mathematical reserve Mortality forecasts## Notes

### Acknowledgements

We are grateful to Geert Coene and Bas Werker for useful discussions about the various models used in this work. We are grateful to the Human Mortality Database and the Office Fédéral de la Statistique for having provided us with the tables used in this work.

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