Term catalog

The term catalog has one row per financial term, generated from the term pages themselves, so this table and the five-blocks table on Contracts as compositions cannot differ. Each row gives the financial term’s signature and parameters, what it does to a year event loss table (YELT), what it consumes and produces, and what state it holds while doing it. The five terms are the ones the dissection identifies in Contract 1. The link opens the full treatment: the formula, its effect on Trial 9 in isolation, a runnable implementation, and the exceedance probability (EP) curves it produces across the 20-trial demo tier.

Term	Signature	Parameters	What it does	State	In → out
Loss filter	$\text{filter}(P)$	$P$: a predicate on the YELT's categorical columns (peril, geography, line of business)	Keeps the rows for which $P$ is true and drops the rest; no loss value changes	Pointwise: each row on its own	YELT → YELT
Contract period	$\text{period}(t_0, t_1)$	$t_0, t_1$: inception and expiry dates	Drops occurrences whose timestamp falls outside inception-to-expiry (a losses-occurring basis)	Pointwise, on the timestamp	YELT → YELT
Scaling	$\text{scale}(f)$	$f$: the factor (the cession $q$ or the participation $p$)	Multiplies every loss by a constant: a quota share's cession inside a composition, the participation share at roll-up; the distribution keeps its shape and every metric scales linearly	Pointwise	YELT → YELT
Occurrence excess	$\text{occ}_{\text{excess}}(A, \ell)$	$A$: attachment; $\ell$: limit	Pays $\min(\max(L - A, 0), \ell)$ on each occurrence independently	Per occurrence: no state across occurrences	YELT → YELT
Aggregate excess	$\text{agg}_{\text{excess}}(A, \ell)$	$A$: aggregate attachment; $\ell$: aggregate limit	Applies the attachment and limit to the trial's running total, booking each occurrence's erosion of the layer as its output row	Per trial: running aggregate in claims order	YELT → YELT (by erosion)

Every term is YELT in, YELT out: it consumes the YELT’s rows (one per occurrence, cedent, geography, and line of business) and produces rows at the same resolution. The two excess terms act on totals and back-allocate their gross to those rows, as the occurrence excess and aggregate excess pages work through, so any term can follow any other without an adapter. Order is part of the definition. What the order changes is the result, not whether the composition is valid: applying an occurrence limit before the cession is not the same as applying the cession first. A contract is such a composition, written $C = T_k \circ \cdots \circ T_1$ and read right to left: $T_1$ applies first. The contract catalog lists the compositions the canonical contract types are built from; Contracts as compositions explains the algebra, and the conventions the terms rely on (contracts at 100%, claims-order erosion, the subject-side event limit) are indexed on Scope, conventions & assumptions.