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December 19, 2020 at 4:13 pm #1487
I have been reviewing classical experience studies performed by other colleagues and considering how material the choice of exposure methodology is to the results. I read the Jan 2019 revision to the SOA’s Experience Study Calculations and found it to be very helpful. However, I am struggling to understand the ways the Balducci Hypothesis (BH) and uniform distribution of deaths (UDD) assumptions were explained in the paper. To me, it seems as if almost all of the paper treats them one way, in the context of the annual and distributed exposure methods, and then section 9 treats them a different way.
Throughout the paper, the annual and distributed methods are explained as being very similar except for how policies that terminate due to the decrement under study in the early/first segment of the policy year allocate the exposures. As an example, the annual method would assign 1 & 0 to the first & second segments, while the distributed method would assign 0.75 & 0.25 to the first & second segments. Other than this, the paper treats them as the same in their exposure calculation demonstrations in sections 4, 5, and 17.6.
But in section 9, numerical examples of how the BH and UDD assumptions subdivide exposures are presented on a monthly basis, and this is where it seems to contradict the rest of the paper. The BH assumption is presented as producing exposures which depend on the annual mortality rate. Reproducing the analysis from p.44 in a workbook with live formulas allows one to see that changing the annual rate of 0.12 to anything else changes the allocation of exposure throughout the year. And the UDD assumption is presented on p.45 as producing exposures which are independent of the annual mortality rate. Ex is always 1/12 of the total in each month no matter which annual mortality rate is in effect.
How can all these concepts be true at the same time? The formulas presented in section 9 imply that assuming BH requires the actuary to know the annual rate in effect before calculating exposures, but this is not mentioned anywhere else in the paper. The date math used to calculate exposures without needing the annual mortality rate used throughout the paper would appear based on section 9 to be a unique property of UDD, but this is not mentioned anywhere else in the paper. I have read through other literature and not been able to find clarification. I own copies of Mortality Table Construction (Batten, 1978) and Survival Models and their Estimation (London, 1988) in case referencing from them may help me understand, although reading them only made me more confused on this issue.

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