Papers and reports

IBNR means "Incurred but not reported". The term refers to claims not yet known to the insurer, but for which a liability is believed to exist at the reserving date. That is simple enough in itself, but the four letters contain a wealth of meaning, and of ambiguity. The wealth arises from the fact that IBNR acts as the remainder term in General Insurance reserving. Many things which cannot be dealt with explicitly elsewhere can be left to fall into the IBNR bag — and as a result, one sometimes cannot be sure what it contains, or even is supposed to contain.

Actuarial methods have for a long time been at the heart of life assurance, providing the essential discipline and long-term financial control. But in the last three decades, it has been increasingly realised in the UK that actuarial methods have an important part to play in general insurance as well. Although the time span is for the most part shorter, the business is likewise concerned with the measurement and financial control of risk. The problems of risk assessment and reserving, of solvency and the release of surplus are present in equal measure as with the life side.

Section 2B of the Supplementary Introduction to Volume 1 gives a general description of reserving methodology. In that description, the process of arriving at an estimate of future payments is described as one of constructing a model, fitting it to some set of past observations, and using it to infer results about the future — in this case, the future events we are interested in are the payment of claims. Several distinctions are made between different types of model, including those between deterministic and stochastic models.

This method models the run-off triangle row-by-row and then ties the rows together. Each row, or year of account, is modelled by a Weibull distribution function. This model was suggested by D H Craighead, and so the Weibull distribution function has become to be known as the Craighead curve when it is used in this context. It is not a linear model and the three parameters have to be estimated using an iterative search method. Once this has been done, the ultimate loss ratio for each year of account can be estimated.

This is a description of a reserving method first proposed by D K Reid (1978) and subsequently developed in a series of papers (Reference 1 to 3). It is a very powerful method of most relevance in direct business where data is available subdivided by claim size.

This document forms part of the Claims Reserving Manual, 2nd edition, 1997. It should be considered historic and for evaluative consideration. Reserving methods and techniques have developed since 1997 in actuarial education and research literature and subsequent updates to regulatory requirements apply.

The variability of chain ladder reserve estimates is quantified without assuming any specific claims amount distribution function. This is done by establishing a formula for the so-called standard error which is an estimate for the standard deviation of the outstanding claims reserve. The information necessary for this purpose is extracted only from the usual chain ladder formulae. With the standard error as a tool it is shown how a confidence interval for the outstanding claims reserve and for the ultimate claims amount can be constructed.

Many stochastic claims reserving methods use aggregate data and yield the first two moments (best estimate and standard error) of the outstanding liability. The term "aggregate data" here refers to the total of payments made for each cohort and each stage of development as opposed to the amount of each individual payment. This paper describes an approach which differs from most stochastic reserving methods in both these respects: