Contract catalog

This page is the reference view of the contract catalog: 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 Helios Re contracts that instantiate it. The link opens the full treatment — the composition worked on Trial 9, a runnable implementation, and the contract’s EP curves across the 20-trial demo tier.

Contract	Signature	Parameters	What it does	Helios 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.