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.\r\nThese new requirements will come in force since 1st January 2014 and\r\nwill be by far more risk-sensitive than Solvency I capital requirements\r\n(firstly introduced in the Seventies and only slightly modified in 2002),\r\nthus enabling a better coverage of the real risks run by any insurer.\r\nConsistent methodologies need to be developed in order to describe both\r\nsingle source of risk and the aggregation between them. Focusing on Non-\r\nLife insurers, first results emphasize that technical risk has the greatest\r\nimpact on the capital requirement. At this regard the main target of this\r\npaper is to analyse the risk profile of a multi-line non-life insurer. A risk\r\ntheoretical simulation model is then applied with the aim to estimate risk capital regarding both Premium and Reserve risk. A comparison\r\nhas been performed between a Risk Based Capital, obtained by the ap-\r\nplication of an Internal Risk Model, and the equivalent Solvency Capital\r\nRequirement, as provided by the Solvency II standard formula. It is fur-\r\nther discussed the dependence problem in order to aggregate losses from\r\ndifferent lines of business by different approaches. Numerical results are\r\nalso figured out in the last part of the paper with evidence of different\r\nresults for small and medium-large companies coming from Premium risk\r\nand Reserve risk pointing out the main reasons of these differences.