In a surplus share treaty reinsurance that covers Y% in excess of X, who pays what?

• A. The primary insurer pays X + (1 - Y%) * (Loss - X)
• B. The primary insurer pays X + Y% * (Loss - X)
• C. The primary insurer pays Loss - X
• D. The primary insurer pays X + Loss

Answer: (A)

In surplus share reinsurance, the primary insurer retains a fixed amount X on each loss, and the reinsurer takes a share of any loss that exceeds X. Specifically, the reinsurer pays Y% of the excess (Loss − X), and the primary insurer covers the remaining portion of that excess, while also fully retaining up to X.

So for a total loss L that exceeds X, the primary’s payment is X plus the portion of the excess not covered by the reinsurer: X + (1 − Y) × (Loss − X). The reinsurer pays Y × (Loss − X). This is exactly the form in the correct option.

For example, with X = 1,000,000, Y = 30%, and Loss = 2,000,000, the primary pays 1,000,000 + 0.70 × 1,000,000 = 1,700,000, and the reinsurer pays 0.30 × 1,000,000 = 300,000, totaling 2,000,000.

The other choices don’t reflect this split: they either assign too much to the primary (as if the reinsurer pays less than Y% of the excess), ignore the retention, or add the full loss without the retention component.