3, On page 23, the solution to question 1 states that 325 is due to a lack of decimal places in the commutation functions. I'm not really satisfied with this statement. The two calculations performed are two different calculations:
- One uses a retrospective approach (5,107,7647)
- The other uses a prospective approach (5,107,422)
Assuming that there is no change in the valuation methodology, I believe that it includes the approach used, i.e., if the liability is currently calculated using the prospective approach, that approach should be used to calculate the liability in the next valuation date unless there is a change in the valuation methodology (which is captured by opening adjustments).
The retrospective approach and the prospective approach will only be perfectly equivalent if the premium is calculated using the equilibrium principle and the calculation can cover all components loaded into the premium. It is actually not the case for profit margin as gross premium valuation will normally not reflect it into the calculation, which makes the retrospective and prospective approaches different. This difference represents the actual profit margin released over time.
Therefore, from my point of view, I think the premium of 800 is not the equilibrium premium, covering only mortality and expense. The 325 should be better regarded as the release of profit loaded in the premium.
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