Quantifying Reserve Risk Based on Volatility in Triangles of Estimated Ultimate Losses

This paper advances the theory and methodology for quantifying reserve risk. It presents a formula for calculating the variance of unpaid losses that is based on analyzing volatility in a triangle of estimated ultimate losses. Instead of examining variability in paid or case incurred loss development, this approach focuses on the estimated ultimates. This builds on previous work by Rehman and Klugman (2010), Rehman (2016), and Seigenthaler (2019). It provides an estimate of one-year reserve risk that extends the total run-off reserve estimate presented in Rehman and Klugman. This paper addresses problems that can arise when the variance-covariance matrix in the Rehman and Klugman formula is computed from a triangle without considering that the vectors for different development ages have different sizes. These problems can give rise to unstable and anomalous results. Finally, this paper provides an estimate of parameter error. Although the methods in this paper do not capture all elements of reserve risk, they do provide a practical way to quantify the risk that is manifest in the volatility of the triangle of estimated ultimate losses.