CDL Terms

Terms generally reduce claims. If you consider a claim as a vertical quantity, deductibles generally take the lower portion while sublimits take the higher portion. What remains in the middle continues on to the covers. The reduction from a deductible = D, and the reduction from a sublimit = X.

The input to a term is the loss from claims to the constrained subject of the term (S), as well as D and X of its "Child" terms in the tree. The output of a term is also an (S,D,X) vector, or (S.out, D.out, X.out).

Sublimits

To process sublimits, we must know the effect of the sublimit acting on the claim, as well as how that interacts with the incoming X of prior terms.

The effect of the sublimit acting on the claim is given as X = Max(S-D-A, 0) where S is the subject claim of the sublimit, D is input from prior terms, and A is the amount of the sublimit. Sublimits act net of deductible.

Deductibles

Deductibles can be somewhat more complicated than sublimits, but let’s take the standard case first. The operation is similar to sublimits. We need to know the effect of the deductible acting on the claim, as well as how that interacts with prior terms.

The effect of the standard deductible acting on the claim is given as D = min(S,A). Franchise deductibles have a slightly different effect: If(S > A, 0, S).

“Max” deductibles have the opposite interaction from standard (or min) deductibles, ensuring the deduction is no more than a certain amount. For a max deductible, we take the minimum of the incoming D and the D produced by the deductible in isolation.

Net of Terms

Net of terms (R for recoverable) can be computed as R = S - D – X.