On Approximating the Individual Risk Model

Peter Kornya

North American Actuarial Journal, 2007, vol. 11, issue 2, 77-98

Abstract: Error bounds are developed for Kornya-Presman–type approximations to the individual risk model. In particular, error bounds are given for the compound Poisson approximation, with the Poisson parameter equal to the expected number of claims.The approximations considered are a modification by Hipp of an approximation originally developed by Kornya, as well as Kornya’s original approximation. The error bounds are similar in concept to Hipp’s original error bounds using concentration–functions, as refined by Čekanavičius, Roos, and others. Computation of the bounds, however, is considerably simplified. In particular, concentration function type bounds called width-norm bounds are calculated directly from the values of the approximation, avoiding completely the need for calculating a special auxiliary compound Poisson distribution. Two examples are given.Depending on the portfolio parameters, the width-norm error bounds may or may not be sharper than the Hipp-Roos error bounds. In any event, it is recommended that the simpler widthnorm calculation, possibly together with an increase in the order of the approximation, be considered in practical applications if the goal is to achieve a specified accuracy with the least amount of computation.For large portfolios, where the maximum claim on any one policy is relatively small compared to the expected aggregate claims, the width-norm error bounds compare quite favorably with error bounds developed by De Pril and by Dhaene.

Date: 2007
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10920277.2007.10597449 (text/html)
Access to full text is restricted to subscribers.

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:taf:uaajxx:v:11:y:2007:i:2:p:77-98

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/uaaj20

DOI: 10.1080/10920277.2007.10597449

Access Statistics for this article

North American Actuarial Journal is currently edited by Kathryn Baker

More articles in North American Actuarial Journal from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().