Internal model techniques of premium and reserve risk for non-life insurers

Solvency II Directive in 2009 has introduced a risk-based solvency requirements for insurance companies across European market. These new requirements will come in force since 1st January 2014 and will be by far more risk-sensitive than Solvency I capital requirements (firstly introduced in the Seventies and only slightly modified in 2002), thus enabling a better coverage of the real risks run by any insurer. Consistent methodologies need to be developed in order to describe both single source of risk and the aggregation between them. Focusing on Non- Life insurers, first results emphasize that technical risk has the greatest impact on the capital requirement. At this regard the main target of this paper is to analyse the risk profile of a multi-line non-life insurer. A risk theoretical simulation model is then applied with the aim to estimate risk capital regarding both Premium and Reserve risk. A comparison has been performed between a Risk Based Capital, obtained by the ap- plication of an Internal Risk Model, and the equivalent Solvency Capital Requirement, as provided by the Solvency II standard formula. It is fur- ther discussed the dependence problem in order to aggregate losses from different lines of business by different approaches. Numerical results are also figured out in the last part of the paper with evidence of different results for small and medium-large companies coming from Premium risk and Reserve risk pointing out the main reasons of these differences.