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Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting

Published online by Cambridge University Press:  29 August 2014

Rudolf Grübel  and
Renate Hermesmeier
Rudolf Grübel*
Affiliation:
Universität Hannover
Renate Hermesmeier
Affiliation:
Universität Hannover
*
Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, e-mail:[email protected]
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Abstract

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Numerical evaluation of compound distributions is one of the central numerical tasks in insurance mathematics. Two widely used techniques are Panjer recursion and transform methods. Many authors have pointed out that aliasing errors imply the need to consider the whole distribution if transform methods are used, a potential drawback especially for heavy-tailed distributions. We investigate the magnitude of aliasing errors and show that this problem can be solved by a suitable change of measure.

Keywords

Total claim size distributionruin probabilitiesrandom sumsFourier transformationaliasingchange of measure
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 2 , November 1999 , pp. 197 - 214
Copyright
Copyright © International Actuarial Association 1999

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