Panjer recursion dating history

Panjer recursion is a member of the following lists: Actuarial science, Theory of probability distributions and Compound distributions.

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The Panjer recursion is an algorithm to compute the probability distribution approximation of a compound random variable
S
=
∑
i
=
1
N
X
i
{\displaystyle S=\sum _{i=1}^{N}X_{i}\,}
where both
N
{\displaystyle N\,}
and
X
i
{\displaystyle X_{i}\,}
are random variables and of special types. In more general cases the distribution of S is a compound distribution. The recursion for the special cases considered was introduced in a paper
by Harry Panjer (Distinguished Emeritus Professor, University of Waterloo). It is heavily used in actuarial science (see also systemic risk).