Severity Curve Fitting for Long-Tailed Lines: An Application of Stochastic Processes and Bayesian Models

I present evidence for a model in which parameters fit to the severity distribution at each report age follow a smooth curve with random error. More formally, this is a stochastic process, and it allows us to estimate parameters of the ultimate severity distribution. I detail a Bayesian hierarchical model that takes a modestly sized dataset of triangulated individual claim data and returns posterior distributions for the parameters of the ultimate severity distribution, trend and loss to an excess layer. Currently available methods are also discussed. Full code and data are provided in the appendices.