Modelling Non-Life Dependencies Using Risk Factor Models

An internal model under Solvency II requires stochastic modelling of the losses of a (re)insurance undertaking. In the context of non-life insurance risk in particular, random variables represent the losses of different portfolios. In order to derive an aggregate distribution, modelling the dependencies between those portfolios is crucial as it determines the diversification. In this talk we present a dependency model for non-life insurance risk based on a decomposition of portfolio losses into risk factor contributions as proposed by Ferriero (DOI: 10.21314/JOR.2021.025). We will discuss possible modelling choices allowing to apply such a model to a (re)insurance portfolio. Calibrating any dependency model in a (re)insurance context is notoriously difficult due to the scarcity of data. To address this challenge, we propose a calibration methodology for such risk factor models using a Bayesian Inference approach. It combines prior distributions, observations and expert judgment, extending a methodology proposed by Arbenz and Canestraro (DOI:10.2143/AST.42.1.2160743).