On The Approximation of the Total Amount of Claims

T. Pentikäinen

ASTIN Bulletin, 1977, vol. 9, issue 3, 281-289

Abstract: Several “short cut” methods exist to approximate the total amount of claims ( = χ) of an insurance collective. The classical one is the normal approximationwhere and σx are the mean value and standard deviation of x. Φ is the normal distribution function.It is well-known that the normal approximation gives acceptable accuracy only when the volume of risk business is fairly large and the distribution of the amounts of the individual claims is not “too dangerous”, i.e. not too heterogeneous (cf. fig. 2).One way to improve the normal approximation is the so called NP-method, which provides for the standardized variable a correction Δzwhereis the skewness of the distribution F(χ). Another variant (NP3) of the NP-method also makes use of the moment μ4, but, in the following, we limit our discussion mainly to the variant (2) (= NP2).If Δz is small, a simpler formulais available (cf. fig. 2).Another approximation was introduced by Bohman and Esscher (1963). It is based on the incomplete gamma functionwhere Experiments have been made with both formulae (2) and (4); they have been applied to various F functions, from which the exact (or at least controlled) values are otherwise known. It has been proved that the accuracy is satisfactory provided that the distribution F is not very “dangerous”.

Date: 1977
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cup:astinb:v:9:y:1977:i:03:p:281-289_00

Access Statistics for this article

More articles in ASTIN Bulletin from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Kirk Stebbing ().