Uniform Distribution of Deaths, Fractional Independence, and Negative Payment-Frequency*

Hans U. Gerber and Elias S. W. Shiu

North American Actuarial Journal, 2025, vol. 29, issue 2, 478-493

Abstract: Under the assumption of a uniform distribution of deaths (UDD), the expected present value of a life annuity with level payments payable m times a year can be expressed in terms of that payable once a year, together with some quantities that depend on interest only. By studying the expected annuity cashflows in the year of death, we determine the financial meaning of these interest-only quantities. Our analysis can be extended to the more general assumption of fractional independence (FI). Under the FI assumption, we express premium and reserve formulas for insurance with premiums payable m times each year in terms of those with premiums payable only once each year. We also discuss an intriguing concept called negative payment-frequency.

Date: 2025
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DOI: 10.1080/10920277.2024.2385384

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