When new business is written, the value of the company may reduce (when viewed on a regulatory basis) even if the business is likely to be profitable. This is known as New Business Strain. Zillmerisation is one method of adjusting a net premium valuation to ease this initial valuation strain.
More specifically when doing a net premium valuation, for a policy taken at age x, t years into the policy:
reserve = S . A(x+t:n-t) - NP(x:n) a(x+t:n-t)
= 0 at time t=0 (by definition of NP)
where S is the sum assured (face amount), A is an assurance function, NP is the net premium for that sum assured, a is an annuity function, E is the initial expenses (i.e. PV of future benefits less PV of future notional net premiums)
In applying a Zillmer adjsument, NP is increased by an amount E/a(x:n)
so that the reserve at time t=0 is -E
A variation on the Zillmer adjustment is the Sprague adjustment:
If we assume the first year of premium doesn't count (because it's being used up on those initial costs), we can change the reserve as follows:
reserve = A(x+t:n-t) - NP(x+1:n-1) a(x+t:n-t) (i.e. PV of future benefits less PV of different notional net prem)
Since the adjusted net premium is larger, you are in effect subtracting a larger amount, producing a smaller reserve - and thus reducing the new business strain.