Solvency 2: an analysis of the underwriting cycle with piecewise linear dynamical systems

An actuarial model will beemployed in order to correctly model the underwriting cycle for non-life insurance companies, also taking into account the effect on thesolvency ratio adopting an approach based onpiecewise–linear dynamical systems, in orderto investigate also the long time horizon dynamic of the model. The basic model is derivedfrom Collective Risk Theory. Besides a dynamic control policy (see Pentikainen et al., 1989),this permits to specify the relationship betweensolvency ratio and safety loading, in order tomodel the underwriting cycle. In particular asimplified formula of safety loading is derivedthat assumes the form of a one dimensionalpiecewise linear map, whose state variable isthe solvency ratio.