Simplified Confidence Boundaries Associated with Calendar Year Projections

Actuaries may use various simulation and risk theoretic techniques to assess the variability in loss reserves. However, non-actuaries are often involved in the selection of the reserve liability "point estimate", but they may not have as firm an understanding of the level of uncertainty implicit in the book of business. They often ignore the potential impact of reserve fluctuations due to the lack of any meaningful measure of a range of variability from their perspective. Perhaps a simpler measure of implicit variability is required. This paper will describe a method which invokes small sampling theory to derive empirical confidence intervals about expected age-to-age LDF’s. These interval LDF’s are used to generate "simplified (upper and lower) confidence boundaries" associated with various calendar year projections. The results, when graphed yield an intuitive summary of the impact and nature of priors years’ incurred effects to the income statement. These simplified confidence boundaries can be used to define the basis of a convenient hindsight test. Most importantly, the graphs may impart to non-actuaries a view of the levels of reasonable fluctuation that may be expected in the estimation of the mean of a stochastic process. Other key words: reserving, confidence estimates.