On the robust stability of pricing models for non-life insurance products

One of the most significant and challenging problems in actuarial practice, especially for general insurance, is the modelling of the premium pricing process and furthermore its stability. The classical actuarial approach to calculating the premium simply covers the expected claims, with an increase for eventual expected surplus, chosen such that the portfolio can be considered stable. In this paper, we present an alternative model for the premium pricing process of a portfolio consisting of different non-life products. Moreover, a standard decision function for the determination of the premium is proposed based on the recent claim experience and a negative feedback mechanism of the known surplus value. The investigation of the robust stability of the system is performed via a Linear Matrix Inequality (LMI) criterion, permitting extensions of existing results. The novelty of the approach consists in the use of tools from the robust analysis of engineering systems in the insurance pricing process of non-life products into a discrete-time framework.