Panjer recursion: Difference between revisions

Revision as of 16:56, 17 March 2013

Revision as of 14:23, 17 February 2014

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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 of [[Harry Panjer]].<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> It is heavily used in [[actuarial science]].

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: <math>f_k = P[X_i = hk].\,</math>

In actuarial practice, <math>X_i\,</math> is obtain by discretisation of the claim density function (upper, lower...).

=== Claim number distribution ===