Application of Collective Risk Theory to Estimate Variability in Loss Reserves

Summarizes the collective risk model and ways to compute aggregate loss distributions. Considers parameter uncertainty and provides a bibliography concerning stochastic approaches to reserve estimation. Abstract: The intent of this paper is to present an introduction to Collective Risk Theory for the first time reader and considerations in applying that theory to estimate variability in loss reserves. It begins with a brief introduction to the basic concepts of Collective Risk Theory along with a survey of some of the techniques developed to date to estimate the aggregate distribution of losses. With this framework, descriptions of some applications to loss reserves are discussed, with attention paid to the assumptions inherent in those methods and some problems that arise in applying this theory to reserves. Of note are questions that are not directly addressed by this model; in particular, parameter uncertainty. Included are references which, it is hoped, will lead the interested reader further into the applications to date.