Parameter uncertainty and reserve risk under Solvency II

Abstract

In this article we consider the parameter risk in the context of internal modelling of the reserve risk under Solvency II.We point out that the objectives of risk capital calculations differ from those of classical reserving and conclude that standard methods of classical reserving focusing on the estimation error of claims reserves are in general not appropriate to model the full impact of parameter uncertainty for the reserve risk.Referring to the requirements of Solvency II we assess different methods to model parameter uncertainty for the reserve risk by comparing the attained probability of solvency with the required confidence level. We provide evidence that the popular bootstrapping approach is not appropriate to model parameter uncertainty for the reserve risk according to this quantitative assessment.For the normal model we present an adaption of the approach proposed in Fröhlich and Weng (2015) based on an analytical result and derive a risk capital model attaining the required confidence level in good approximation. Furthermore, for the lognormal model experimental results suggest that even a direct application of the method proposed in Fröhlich and Weng (2015) clearly outperforms the bootstrapping approach according to the quantitative criterion mentioned above.