Panjer recursion: Difference between revisions

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The '''Panjer recursion''' is an [[algorithm]] to compute the [[probability distribution]] approximation of a compound [[random variable]]

<math>S = \sum_{i=1}^N X_i\,</math>.

where both <math>N\,</math> and <math>X_i\,</math> are [[random variable]]s 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 <ref>{{cite journal|last=Panjer|first=Harry H.|year=1981|title=Recursive evaluation of a family of compound distributions.| journal=ASTIN Bulletin|volume=12|issue=1|pages=22–26|publisher=[[International Actuarial Association]]|url=http://www.casact.org/library/astin/vol12no1/22.pdf|format=PDF}}</ref> by [[Harry Panjer]] ([[Distinguished Emeritus professorProfessor]], [[University of Waterloo]]<ref>[http://www.actuaries.org/COUNCIL/Documents/CV_Panjer.pdf CV], actuaries.org; [https://math.uwaterloo.ca/statistics-and-actuarial-science/about/people/harry-panjer Staff page], math.uwaterloo.ca</ref>). It is heavily used in [[actuarial science]] (see also [[systemic risk]]).

== Preliminaries ==