Subject premium
The gross premium base on which a non-proportional treaty premium is calculated by applying a rate.
Textbook case: on 30 million euros of subject premium, a rate of 1.5 per mille gives a treaty premium of 45,000 euros. Subject premium is the cedant's gross premium base used to calculate the treaty premium for an excess-of-loss or stop-loss cover. Treaty premium = rate × subject premium. The base stands for the total underlying exposure covered by the layer, and burning cost and rate on line are calculated off it. Its definition gets negotiated word by word. Does it include premiums net of brokerage? Taxes? Premiums from all lines, or from one specific line? Define it loosely and you leave room for argument over what the treaty actually covers.
Textbook case: a cat XL treaty on a household book. Subject premium of 30 M EUR at a rate of 1.5‰ gives a treaty premium of 45,000 EUR. For burning cost, divide the 450,000 EUR of layer losses by the 30 M EUR of subject premium and multiply by 1,000, which gives 15‰.
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