Robust estimation
Classical statistical procedures act on strict parametric model assumptions which may not be fulfilled in real world situations. Tukey has shown that already under tiny deviations from model assumptions, here from normality, the mean deviation may perform better than the standard deviation, the latter being efficient under strict normality.
Classical estimators often behave pathologically and react sensitive to outliers. Robust statistical concepts deal with the stability of statistical procedures in the neighborhood of ideal models, react less sensitive to perturbations and provide in many cases consistent results.
Neuronal networks
We apply neural nets for predictive modeling in the context of claims reserving and premium calculation.
Unbiased estimation
In general, capital requirements are evaluated using the so-called plug-in approach. Estimated parameters are plugged into the distribution functions to determine the capital requirements assuming that the parameters are ‘correct’. The capital needs may be underestimated. The parameter uncertainty may be considered heuristically by means of a conservative calibration. However, this approach does not give any hint on the level of parameter uncertainty. The latter may be accounted for explicitly applying unbiased estimation procedures.
Inflation
Assessments of claims reserves consider inflation in general just implicitly. Calendar year effects are regularly neglected. The analyses do not go back in time sufficiently to address the high inflation in the 70s and 80s of the last century some 50 years ago. However, inflation indices may be modelled with vectorautoregressive processes. Several inflation indices can be projected simultaneously into the future. The dependence between the indices feeds through to the results.