Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk

Definition 13.7 (Non Degenerate Discrete Distribution)

A discrete distribution that is normalized is called non degenerate if holds for all n ∈ .

In addition, it will be useful to define the class of discrete distributions known as the Panjer class.

Definition 13.8 (General Panjer Class of Discrete Distributions)

A discrete distribution with parameters a, b ∈ and order k ∈ is in the Panjer class if for all n ≤ k – 1 and the probabilities satisfy the recursion

(13.93)

for all n ≥ k. Such a class of discrete distribution that satisfies this condition is known as a Panjer class family with parameters a, b and order k.

There will be further discussion on these classes of discrete ...