Zillmerization as a Method of Gross Premium Reserve Calculation

Due to its outstanding importance we discuss the mathematical relations of zillmerization in detail, in a separate chapter. Zillmerization can be regarded as general practice in Hungary, so when calculating the gross premium reserve of regular premium insurances we cannot leave it out.

At first zillmerization only affected the first year’s premium, today it can theoretically affect even that f the past year. This way we’ll examine separately the classical (“conservative”) approach and today’s approach.

1. Zillmerization means borrowing part of the premium (or the premium reserve) of the first year at the beginning of the term, that will be repaid later on from the premium loadings in equal annual instalments. Because of this, an important element of the conservative approach is that zillmerization concerns strictly only annual premium payment policies.

2.  The “conservative approach” in the title also means that a “natural” limit is set to the borrowing of the premium. According to this, the maximum sum borrowed can be a part of the first year’s gross premium so that the remaining part of the premium still covers the continuous expenses142 and the first year’s death benefits.

3. Consequently before premium payment the premium reserve is zero, and after premium payment even at the commencement of the insurance and at the first anniversary it is a positive value, since a part of the first net premium, and the second (greater) net premium totally goes to the reserve, and perhaps even the 

4. Because in the “modern” practice this limit is not followed, which very often causes the reserve of the first anniversary to be zero (i.e. neither the first, nor the second premium fills the reserve above the part covering the death benefit payments of the given year).

5. The result is not surprising if we remember that the term fix insurance can be regarded as an endowment insurance with varying sum assured, which has a death sum assured equal to the value of the maturity benefit discounted to the time of death (and were the death benefit is – according to the policy – immediately changed to a single premium term fix insurance).