Estimating the Variability of Loss Reserves

This paper presents two major refinements to common practices in estimating the variability of loss reserves. The first is specification of a closed form density function that very closely approximates the aggregate loss distribution resulting from the convolution of the typical frequency and severity distributions—even at the extreme tails. This new distribution apparently has the following useful properties: (1) the sum of two of these distributions is also a distribution of the same form, regardless of whether the original distributions are independent or correlated; and (2) the values of the coefficients of the combined distribution is a function of the coefficients of the original distributions. These two properties should significantly streamline the process of determining the aggregate distribution for loss reserves. This paper openly questions the validity of the practice of approximating the confidence level factors for the aggregate distribution of loss reserves by using those factors from the aggregate distribution of all claims incurred for one (or more) accident years. It presents an alternative approach that avoids the likely inaccuracies of this common practice by using the new density function to represent: 1) the variability of each accident year piece of the loss reserve (at successive, advancing ages) and 2) the variability of the sum of these pieces.