Provisions techniques et capital de solvabilité d'une compagnie d'assurance : méthodologie d'utilisation de Value-at-Risk

The advent of the future European prudential framework (Solvency II) and, to a lesser extent, of the phase II of the IFRS dedicated to the insurance contracts, will systematize the use of the Value-at-Risk (VaR) risk measure in insurance. Especially used for financial purposes, the measure of an insurance risk by a VaR technique requires a specific adaptation. Schematically we may distinguish two different contexts, which impose distinct approaches : * the measurement of the risk related to the sinistrality by the use of a VaR in the heart of the probability distribution : the technical provision will have to be enough to pay the claims with a 75 % probability ; * the measurement of risk related to the ruin of the company by the mean of a very high order VaR : the solvency capital must to be calibrated to control the ruin if the insurer with a probability higher than 99.5 %. In the first situation, the two standard approaches (historical VaR or modelling the sinistrality) can be based on a statistical material of relative but sufficient size to estimate a VaR in the heart of the probability distribution. In the second case, we are confronted to the absence of observations. Also we have to model the basic variables which influence the solvency of the company in order to be able to simulate the ruin of the company and finally to estimate the high order VaR. This last stage will require the use of Extreme Value Theory. In this paper, we present the contexts of VaR computation in insurance, the related probabilistic results and the limits of these kinds of criterion for insurance purposes.