Piecewise linear dynamic systems for own risk solvency assessment

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. Consid-ering also the advices in CEIOPS Consultation Paper 56, a natural extension of thisprocedure is to employ IRM in Own Risk Solvency Assessment (ORSA) also in along time horizon. Under an ORSA, insurance companies will have to understandhow their strategic choices affect the solvency ratio. In this analysis the real risk pro-file, risk tolerance and supervisor’s rules can also be included. In this framework,the underwriting cycle could provide an additional volatility source to the liabilitiesdistribution and so it could increase the solvency capital requirement or influencenegatively the profitability of insurance companies and so it could be included insidean IRM. The aim of this paper is to explain how to use Piecewise Linear DynamicSystems under an ORSA process. A dynamic control policy is defined to specifythe relationship between solvency ratio and safety loading, and so to model the un-derwriting cycle. Under some simplifying assumptions, the corresponding dynamicequation for the solvency ratio assumes the form of a one dimensional piecewise lin-ear map. The model could be easily extended to include dividend policies, in orderto control profitability taking into account solvency requirements.