Introduction to Bayesian Loss Development

This paper provides an introduction to the use of Bayesian methods for blending prior information with a loss development pattern from a triangle. The methods build upon conjugate forms discussed in earlier literature but introduce the Generalized Dirichlet as a prior, which allows for a significant simplification in calculation. The discussion is mainly restricted to the question of blending observed data with prior beliefs and not on the question of reserve ranges.

The paper is aimed at practicing actuaries seeking an introduction to Bayesian ideas for loss development. The methods will work with a single development triangle analyzed in a spreadsheet.

Keywords Bayesian loss development, conjugate prior, Generalized Dirichlet