Correlation and the Measurement of Loss Reserve Variability

Loss reserves are the largest liability on the balance sheet of an insurance company, yet they are only estimates. Even the actuary responsible for making the estimates is often unable to quantify the inherent uncertainty. This is partly a consequence of the complexity of estimating the variability of the reserve estimates. Correlation across several dimensions makes statistical measurement of uncertainty difficult. Most insurers have only a limited number of historical data points available with which to make estimates of the multiple correlations, making estimation of correlation problematic. This paper presents a mathematically simple model of loss development variability which allows the inclusion of several types of correlation. It can also be adapted to deal with other complexities which may arise in the analysis of reserves. The paper also presents methods which make it easier to estimate correlations in practical applications.