Piecewise linear dynamic systems for own risk solvency assessment

Abstract

Under Solvency 2, there is a growing need to develop Internal Risk Models (IRM) to get accurate estimates of liabilities under a one-year time horizon. Considering also the advices in CEIOPS Consultation Paper 56, a natural extension of this procedure is to employ IRM in Own Risk Solvency Assessment (ORSA) also in a long time horizon. Under an ORSA, insurance companies will have to understand how their strategic choices affect the solvency ratio. In this analysis the real risk profile, risk tolerance and supervisor’s rules can also be included. In this framework, the underwriting cycle could provide an additional volatility source to the liabilities distribution and so it could increase the solvency capital requirement or influence negatively the profitability of insurance companies and so it could be included inside an IRM. The aim of this paper is to explain how to use Piecewise Linear Dynamic Systems under an ORSA process. A dynamic control policy is defined to specify the relationship between solvency ratio and safety loading, and so to model the underwriting cycle. Under some simplifying assumptions, the corresponding dynamic equation for the solvency ratio assumes the form of a one dimensional piecewise linear map. The model could be easily extended to include dividend policies, in order to control profitability taking into account solvency requirements.