Stochastic Claims Reserving in General Insurance

• Published in: British Actuarial Journal 2002-08, Vol.8 (3), p.443-518
• Main Authors: England, P.D., Verrall, R.J.
• Format: Article
• Language: English
• Subjects: Actuarial science; Approximation; Binomials; Data smoothing; Estimates; Estimation methods; Insurance claims; Modeling; Parametric models; Sessional meetings: papers and abstracts of discussions; Statistical variance; Stochastic models
• ISSN: 1357-3217; 2044-0456; 1748-5002
• DOI: 10.1017/S1357321700003809

This paper considers a wide range of stochastic reserving models for use in general insurance, beginning with stochastic models which reproduce the traditional chain-ladder reserve estimates. The models are extended to consider parametric curves and smoothing models for the shape of the development run-off, which allow extrapolation for the estimation of tail factors. The Bornhuetter-Ferguson technique is also considered, within a Bayesian framework, which allows expert opinion to be used to provide prior estimates of ultimate claims. The primary advantage of stochastic reserving models is the availability of measures of precision of reserve estimates, and in this respect, attention is focused on the root mean squared error of prediction (prediction error). Of greater interest is a full predictive distribution of possible reserve outcomes, and different methods of obtaining that distribution are described. The techniques are illustrated with examples throughout, and the wider issues discussed, in particular, the concept of a ‘best estimate’; reporting the variability of claims reserves; and use in dynamic financial analysis models.