A Multivariate Evolutionary Generalised Linear Model Framework with Adaptive Estimation for Claims Reserving
36 Pages Posted: 2 Jul 2019 Last revised: 7 Jul 2019
Date Written: July 1, 2019
In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are allowed to evolve in a recursive manner, and dependence is incorporated in the specification of these factors using a common shock approach.
We consider factors that evolve across accident years in conjunction with factors that evolve across calendar years. This two-dimensional evolution of factors is unconventional as a traditional evolutionary model typically considers the evolution in one single time dimension. This creates challenges for the estimation process, which we tackle in this paper. We develop the formulation of a particle filtering algorithm with parameter learning procedure. This is an adaptive estimation approach which updates evolving factors of the framework recursively over time.
We implement and illustrate our model with a simulated data set, as well as a set of real data from a Canadian insurer.
Keywords: Claims Reserving, Evolutionary GLM, Adaptive Reserving, Particle Learning, Common Shock Models
JEL Classification: G22
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