Panjer recursion

For the "Panjer recursion", the probability distribution of N has to be a member of the Panjer class, otherwise known as the (a,b,0) class of distributions.

In the context of actuarial science, the distribution appeared in its general form in a paper by K. Hess, A. Liewald and K.D. Schmidt when they characterized all distributions for which the extended Panjer recursion works.

The Panjer recursion makes use of this iterative relationship to specify a recursive way of constructing the probability distribution of S. In the following denotes the probability generating function of N: for this see the table in (a,b,0) class of distributions.