2. MATHEMATICAL PROPERTIES OF TABLE L (continued)

Lemma 1: Given constants r₁ and r₂ with 0 < r₁ < r₂ , define the random variable, L, to be the limited loss restricted to:

  Let L =

Then, E[L]/E = 1+ y *(r1) - f *(r2).

Theorem 1: For any r > 0, y *(r) = f *(r) + r - 1.

In the California WC Retrospective Rating Plan, the retrospective premium, R, is given by:

R = BP + CA* subject to a:   maximum of G, and a   minimum of H

Unlike the NCCI plans, the California Plan uses only one tax expense ratio, so the tax multiplier is included in the basic premium ratio and the LCF.

To demonstrate how Table L leads to a balanced plan, the following is given:

Symbol	Definition
LG	the actual limited losses that will produce the maximum premium. =
rG	the entry ratio for the maximum premium.
LH	the actual limited losses that will produce the minimum. =
rH	the entry ratio for the minimum premium.

L = the losses that will produce the retro premium in the above eq. without reference to max and min premiums. The retrospective premium can be rewritten as:

R = BP + CL

= basic premium + converted losses.

I* = the net Table L insurance charge.

= E(f *(rG) - y *(rH)).

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