Reserving with Incomplete Exposure Information

This paper outlines a reserving method that allows the actuary to use exposure information, such as onlevel premium, even if that information is only available for a limited number of years. The method is a simple blending of methods already in wide use, but can be shown to be based on a common underlying statistical model. The paper provides an overview of the Over-Dispersed Poisson model, and how it relates to Multiplicative LDF, Cape Cod, and Bornhuetter-Ferguson methods.

Motivation: The reserving actuary may have reliable exposure information (e.g., onlevel premium) for only a few recent years of data, rather than for the full historical period for which reserves need to be set.

Method: This incomplete exposure information can still be used, by implementing a hybrid reserving method equivalent to the Cape Cod method for the recent years and the Multiplicative LDF method for older years.

Results: We show how common reserving methods can be derived from a single statistical model, and then show how these methods are best combined when partial information is available.

Conclusions: This is a practical solution to the problem of stabilizing loss projections for recent accident years, incorporating available rate change information, and being responsive to actual loss emergence.

Keywords: Reserving, GLM, Chain ladder, Cape Cod, Bornhuetter-Ferguson.