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The fuzzy Bornhuetter–Ferguson method: an approach with fuzzy numbers

Published online by Cambridge University Press:  22 August 2016

Jochen Heberle  and
Anne Thomas
Jochen Heberle*
Affiliation:
School of Business, University of Hamburg, Von-Melle-Park 5, 20146 Hamburg, Germany
Anne Thomas
Affiliation:
School of Business, University of Hamburg, Von-Melle-Park 5, 20146 Hamburg, Germany
*
*Correspondence to: Jochen Heberle, School of Business, University of Hamburg, Von-Melle-Park 5, 20146 Hamburg, Germany. Tel: +4940428383541; E-mail: [email protected]
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Abstract

This paper shows how the well-known Bornhuetter–Ferguson claims-reserving method can be extended by applying fuzzy methods. The a priori information for the ultimate claims derives from market statistics, organisational data, etc. and might contain vagueness. Likewise, the parameters of the claims development pattern can be vague or are adapted, retrospectively, due to subjective judgement. With the help of fuzzy numbers we develop new predictors for the ultimate claims. Furthermore, we quantify the uncertainty of the ultimate claims for single and aggregated accident years.

Keywords

Claims reservingBornhuetter–FergusonFuzzy numbersUltimate claims predictorFuzzy uncertainty

JEL classification

C10: General G22: Insurance • Insurance Companies • Actuarial Studies
Type
Papers
Information
Annals of Actuarial Science , Volume 10 , Issue 2 , September 2016 , pp. 303 - 321
Copyright
© Institute and Faculty of Actuaries 2016 

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