Contract catalog

The contract catalog has one row per canonical contract type, generated from the contract pages themselves. Each row gives the signature (the composition that defines the type), its parameters, what it does to the subject loss, and the Caldera Re contracts that instantiate it. The link opens the full treatment: the composition worked on Trial 9, a runnable implementation, and the contract’s exceedance probability (EP) curves across the 20-trial demo tier.

Contract	Signature	Parameters	What it does	Caldera Re
Quota share	$\text{QS}(q) = \text{scale}(q) \circ \text{period}(t_0, t_1) \circ \text{filter}(P)$	$q$: cession percentage	Cedes a fixed share $q$ of every covered loss; optional event and annual limits insert an occurrence excess and an aggregate excess before the scaling	C5
Catastrophe excess of loss	$\text{CatXoL}(A, \ell, n) = \text{agg}_{\text{excess}}(0,\; (1+n) \cdot \ell) \circ \text{occ}_{\text{excess}}(A, \ell) \circ \text{period}(t_0, t_1) \circ \text{filter}(P)$	$A$: attachment; $\ell$: occurrence limit; $n$: reinstatements	Clips each occurrence to the layer and caps the annual total at $(1+n) \cdot \ell$, the aggregate limit that encodes $n$ reinstatements	C1, C4, C6
Aggregate excess of loss	$\text{AggXoL}(A, \ell) = \text{agg}_{\text{excess}}(A, \ell) \circ \text{period}(t_0, t_1) \circ \text{filter}(P)$	$A$: aggregate attachment; $\ell$: aggregate limit	Applies the attachment and limit to the trial total: occurrences accumulate against $A$ before the contract responds	C2, C3

Every composition reads right to left (the rightmost term applies first, a loss filter in every entry here) and defines its contract at 100%: participation is applied at portfolio roll-up, never inside a composition. The building blocks are listed in the term catalog. Inuring (what one contract’s recoveries do to another’s subject loss) is a relationship between compositions, not a term of one: see Programs.

What the catalog does not cover

The catalog covers quota share, catastrophe excess of loss, and aggregate excess of loss on the loss side, with the cat model’s event as the occurrence; each structure below needs something the catalog does not have yet, or sits outside this site’s scope.

Structure or provision	Why the catalog cannot express it today	What it needs
An hours clause that groups losses differently from the model event	Two model events inside one window, or one long event split across two windows, change which losses count as one occurrence before any per-occurrence term applies. The catalog takes the model event as the occurrence.	A term: an occurrence definition that regroups the YELT’s rows into occurrences
Franchise deductible and other triggers	A trigger passes the full loss once its condition is met and nothing otherwise; the excess terms pass only the part above the attachment.	A term: the trigger
Count-based nth-event cover	It counts occurrences in claims order, and every catalog term acts on loss amounts. The dollar-drafted form, an aggregate retention of one occurrence limit on an occurrence layer, is already a composition of catalog terms.	A term that counts occurrences
Top & drop	Whether the layer drops down depends on the trial’s first occurrence: whether it reached the top layer, and how far it eroded the layers below.	A relationship between layers, the third besides inuring and forwarding; Programs names it and does not model it, so the programs the chapter’s claim covers are those whose layers inure
Reinstatement premiums	The cedent pays them to restore the limit an occurrence has eroded, pro rata to the amount reinstated and sometimes to time. The CatXoL composition encodes the reinstated limit and leaves the premium out.	Nothing on the loss side: the premium side, outside the loss-side claim
Surplus share and per-risk excess of loss	They cede or attach per policy or location, and the trial losses this site works from are recorded by cedent, geography, and line of business.	Finer data granularity: losses per risk, outside property-cat post-model scope