Spec the Treaty (Solution)

This is the whole thing: the prose treaty turned into a seven-claim battery — the flat cession, the floor, and the untouchable attritional all pinned — plus the two-line Ceded that satisfies it. The exercise hands you the prose and a stub; you write both halves.

The sign rule is trivial. The two interactions are not, and they are where a naïve treaty leaks money.

The two interactions

The flat cession meets a small claim. Rule 1 says cede 100; rule 2 says never cede more than the claim. C1 (gross 80) can only give 80 — ceded −80, net 0, not the naïve net of −20. C6 (gross 90) cedes 90, net 0. A treaty that ignores the cap books a negative loss and hands the reinsurer money that was never at risk.
The flat cession meets the attritional bulk. Rule 3 says a per-claim treaty cannot touch ATT: no individual claim, no cession. Ceded 0, net stays 350 — not the naïve 250. This is the individual-vs-attritional distinction the lesson flags for Lesson 3, and here it is worth two points of net all by itself.

Pin those and the rest is the flat rule: C2 → 140, C3 → 320, C4 → 660, C5 → 1,200.

The frozen battery

Claim	Kind	Gross	Naïve (−100 flat)	Ceded	Net	Why
C1	Individual	80	−20	−80	0	floored — can't cede more than 80
C2	Individual	240	140	−100	140	plain flat 100
C3	Individual	420	320	−100	320	plain flat 100
C4	Individual	760	660	−100	660	plain flat 100
C5	Individual	1,300	1,200	−100	1,200	plain flat 100
C6	Individual	90	−10	−90	0	floored — can't cede more than 90
ATT	Attritional	350	250	0	350	untouchable — no individual claim

The naïve column sums to a book net of 2,540; the correct treaty nets to 2,670 — the extra 130 is exactly the two floors (20 + 10) plus the untouched attritional (100) the naïve version would have wrongly ceded.

The treaty, in two lines

static double Ceded(string claim, string kind, double gross)
{
    if (kind == "Attritional") return 0.0;    // Rule 3 — a bulk sum has no individual claim to cede
    return -Math.Min(100.0, gross);           // Rule 1 (flat 100) capped by Rule 2 (never below 0 net)
}

Math.Min(100, gross) is rules 1 and 2 in one stroke: the flat 100, but never more than the claim. The early return is rule 3. Net is gross + Ceded(...) — still no subtraction.

Live and green

Press Run — seven rows, all green.

Write the treaty as a Ceded function — a flat 100 per individual claim, never more than the claim itself, and no cession at all on the attritional bulk — so every case in the seven-claim battery goes green. Render the battery as a grid of spec sentence, expected net and actual net, with a green count and the 2,670 book net in the header.

The treaty is two lines; the battery is the deliverable that outlives it. Hand those seven pinned nets to any agent — or any colleague — and "cede a flat 100" is no longer open to the two misreadings that cost real money.

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