Actuarial models for estimating non life risks

Loss reserving is one of the most critical actuarial procedures in non-life insurance. This procedure projects losses to their ultimate value and estimates the total reserves. The actual amount of the insurers' liability is initially unknown until all claims are finally settled. Inappropriate actuarial methods may lead to misestimation of the total reserve, which has a significant impact on the insurers' solvency. Each reserving method gives a different estimate for the required reserves which means that the appropriate method will be selected according to the judgement of the actuary. In non-life insurance, the insurer should have reserves, for his future obligations concerning with incurred but not reported claims and incurred but not enough reported. In this thesis, we present new methods for estimating the ultimate claims and the total reserves, according to insurance regulations and the market's needs. Using the data in a log-linear way, robust estimators are applied to the chain ladder procedure. We incorporate robust random coefficients regression models and robust cross-section models for the estimation of the total reserves. These models provide a solution to the problem of outlier claims, which have an effect to the pattern of outstanding claims and lead to misreserving. We present an application of the recursive Kalman filter algorithm, in order to estimate the reserves of an insurance company. A robustified version of this Kalman filter algorithm is also provided. Using quantile regression, which offers a more thorough description of the distribution than the classical least squares estimation, we construct methods for loss reserves estimation. In addition, we propose a loss reserving method for a non-life insurance portfolio consisting by several correlated run-off sub-portfolios that can be embedded within the quantile regression model for longitudinal data. Our numerical results indicate that our proposed loss reserving methods provide more reliable results than the existing ones.