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The Swiss Re Exposure Curves and the MBBEFD Distribution Class1

Published online by Cambridge University Press:  29 August 2014

Stefan Bernegger
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Abstract

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A new two-parameter family of analytical functions will be introduced for the modelling of loss distributions and exposure curves. The curve family contains the Maxwell-Boltzmann, the Bose-Einstein and the Fermi-Dirac distributions, which are well known in statistical mechanics. The functions can be used for the modelling of loss distributions on the finite interval [0, 1] as well as on the interval [0, ∞]. The functions defined on the interval [0, 1] are discussed in detail and related to several Swiss Re exposure curves used in practice. The curves can be fitted to the first two moments μ and σ of a loss distribution or to the first moment μ and the total loss probability p.

Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 27 , Issue 1 , May 1997 , pp. 99 - 111
Copyright
Copyright © International Actuarial Association 1997

Footnotes

1

Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distribution

References

Daykin, C.D., Pentikainen, T. and Pesonen, M. (1994) “Practical Risk Theory for Actuaries”. Chapman & Hall, London.Google Scholar