9.6 The recursive method
Suppose that the severity distribution fX(x) is defined on 0, 1, 2, …, m representing multiples of some convenient monetary unit. The number m represents the largest possible payment and could be infinite. Further, suppose that the frequency distribution, pk, is a member of the (a, b,1) class and therefore satisfies
Then the following result holds.
Theorem 9.8 For the (a, b, 1) class,
noting that x Λ m is notation for min(x, m).
Proof: This result is identical to Theorem 7.2 with appropriate substitution of notation and recognition that the argument of fX(x) cannot exceed m.
Corollary 9.9 For the (a, b, 0) class, the result (9.20) reduces to
Starting values for other ...