A Likelihood Approach to Bornhuetter–Ferguson Analysis

Valandis Elpidorou, Carolin Margraf, María Dolores Martínez-Miranda and Bent Nielsen
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Valandis Elpidorou: Arch Reinsurance Europe Underwriting dac Ireland, Dublin 4, Ireland
Carolin Margraf: Cass Business School, University of London, London EC1Y 8TZ, UK
María Dolores Martínez-Miranda: Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain
Bent Nielsen: Nuffield College, University of Oxford, Oxford OX1 1NF, UK

Risks, 2019, vol. 7, issue 4, 1-20

Abstract: A new Bornhuetter–Ferguson method is suggested herein. This is a variant of the traditional chain ladder method. The actuary can adjust the relative ultimates using externally estimated relative ultimates. These correspond to linear constraints on the Poisson likelihood underpinning the chain ladder method. Adjusted cash flow estimates were obtained as constrained maximum likelihood estimates. The statistical derivation of the new method is provided in the generalised linear model framework. A related approach in the literature, combining unconstrained and constrained maximum likelihood estimates, is presented in the same framework and compared theoretically. A data illustration is described using a motor portfolio from a Greek insurer.

Keywords: chain ladder; Bornhuetter–Ferguson; maximum likelihood; exponential families; canonical parameters; prior knowledge (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
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