Un approccio quantile regression per la tariffazione danni, basato su un modello a due parti

In Solvency II (SII) the value of insurance technical provisions shall correspond to the current amount insurance undertakings would have to pay if they were to transfer their insurance and reinsurance obligations immediately to another insurance or reinsurance undertaking. The value of each technical provision holds by an insurance undertaking shall be equal to the sum of a best estimate (BE) and a risk margin (RM). According to SII standard formula the RM is a function of the Solvency Capital Requirement (SCR) shall correspond to the VaR of the basic own funds subject to a confidence level of 99.5\% over a one-year period. This methodology is fully coherent with a standard actuarial approach used in accordance with the prudent person principle and generally applied in a pure premium calculation. The pure premium is an estimate of the expected loss plus an implicit or explicit loading requested as a risk margin compensation for expected deviation from the mean. We focus on a specific non-life insurance risk: the premium risk. The SII standard formula requires the assessment of SCR, and consequently of a RM, at most for a single Line of Business (LoB) while avoids to determine (it is out of SII scope) the same amounts for each risk in portfolio. In some LoB in addition to focusing on the aggregate, it is important for the actuary to be able to develop a balanced indication of the pure premium (BE+RM) for individual risks or risk segments, too. In actuarial practice, the classification ratemaking is performed usually via Generalized Linear Model. GLM defines only the estimate of the conditional best estimate of the liabilities. In order to investigate the individual risk margin, we use a pricing model based on the two part model Quantile Regression, to perform a classification ratemaking. The Quantile Regression leads to the estimate of a conditioned percentile, hence, permits a better measurement of the variability inherent in the risk profiles and is compliant with SII.