The European Project Solvency II is devoted to the appraisal of a Solvency Capital Requirement that shouldcapture the overall risk profile of insurance companies. In this framework there is a growing need to developso-called internal risk models to get accurate estimates of liabilities. In the context of non-life insurance, it iscrucial to correctly assess risk from different sources, such as underwriting risk with particular reference topremium, reserving and catastrophe risks. In particular the underwriting cycle is not quantified in standardformula under Quantitative Impact Study 4, but probably it could be included, as it provides additionalvolatility to liabilities distribution and so it could increase the capital requirement.The aim of this paper is to correctly model the underwriting cycle for non-life insurance companies, alsotaking into account its effect on the solvency ratio. Starting from Collective Risk Theory, a dynamic controlpolicy is defined to specify the relationship between solvency ratio and safety loading, to model theunderwriting cycle. The corresponding dynamic equation for the solvency ratio, under some assumptions,assumes the form of a one dimensional piecewise linear map. In the first part of the work a deterministicversion of this map is analyzed, where aggregate losses are simply regarded as a parameter. Numericalanalysis and stochastic assessments of the model conclude the work.
A dynamic analysis of the underwriting cycle in non-life insurance
CERCHIARA, Rocco Roberto;LAMANTIA F. G.
2009-01-01
Abstract
The European Project Solvency II is devoted to the appraisal of a Solvency Capital Requirement that shouldcapture the overall risk profile of insurance companies. In this framework there is a growing need to developso-called internal risk models to get accurate estimates of liabilities. In the context of non-life insurance, it iscrucial to correctly assess risk from different sources, such as underwriting risk with particular reference topremium, reserving and catastrophe risks. In particular the underwriting cycle is not quantified in standardformula under Quantitative Impact Study 4, but probably it could be included, as it provides additionalvolatility to liabilities distribution and so it could increase the capital requirement.The aim of this paper is to correctly model the underwriting cycle for non-life insurance companies, alsotaking into account its effect on the solvency ratio. Starting from Collective Risk Theory, a dynamic controlpolicy is defined to specify the relationship between solvency ratio and safety loading, to model theunderwriting cycle. The corresponding dynamic equation for the solvency ratio, under some assumptions,assumes the form of a one dimensional piecewise linear map. In the first part of the work a deterministicversion of this map is analyzed, where aggregate losses are simply regarded as a parameter. Numericalanalysis and stochastic assessments of the model conclude the work.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
