The analysis of "all-prior" data
Some data sources, such as the NAIC Annual Statement – Schedule P as an example, contain a row of all-prior data within the triangle. While the CAS literature has a wealth of papers that have developed various methods for estimating tail factors, and the CAS Tail Factor Working Party recently published a report on tail factor methods, tail factors are not directly applicable to all-prior data. Absent a defined methodology, it seems to be common practice for an analysis of data triangles that include an all-prior row to either exclude the all-prior data or to make the explicit assumption that the case reserves, or case plus IBNR reserves, for these claims are adequate. This may be reasonable in certain situations but given the potential materiality of this part of the reserve it would be a useful addition to the actuary’s toolkit to develop some methods for analyzing the all-prior data or for testing the reasonability of assuming the case reserves, or case plus IBNR reserves, are adequate.
The process followed in this paper is to both graphically and formulaically illustrate the data issues and analysis, then apply the concepts of a well-known method with three different data sets. While only a deterministic point estimate method is illustrated in this paper, the framework should be quite easily adaptable to other deterministic methods or stochastic models.
This article was published in the Fall 2014 issue of E-Forum, a Casualty Actuarial Society publication.