The Analysis and Estimation of Loss & ALAE Variability: A Summary Report

Motivation: Casualty Actuaries have long been interested in the estimation of ultimate losses and ALAE. The potential variability of the ultimate outcome is critical to understanding the extent of the risks faced by the risk-bearing entity that either has adopted or is contemplating the adoption of loss and ALAE estimates. Over the years many people (actuaries and others) have made significant contributions to the literature and overall discussion of how to estimate the potential variability of ultimate losses, but there is no clear preferred method within the actuarial community. This research paper is an attempt to bring all of the historical research together in one cohesive document.

Method: The Working Party worked exclusively via e-mail and a private area of the CAS web site. After a joint effort to assemble an outline, the Working Party separated into subgroups, each assigned to prepare one of the sections of this paper.

Results: There are many approaches to estimating future payments for property and casualty liabilities, many of which have stochastic roots leading to not only an estimate of future payments but also of the distribution of those payments. However, we found no single method that is clearly superior. We have identified some areas of potential future research.

Conclusions: The actuarial profession does not yet have a single, all inclusive method for estimating the distribution of future payments for property and casualty liabilities. Much work is yet to be done on the issue.

Availability: A copy of the Working Party’s paper can be found on the CAS web site at http://www.casact.org/pubs/forum/05fforum/

Keywords: Reserve Variability; Future Payment Variability; Generalized Linear Model; Delta Method; Over-Dispersed Poisson Model; Bootstrap; Bayesian Inference; Markov Chain Monte Carlo