Kurtosis

and skewness estimation for non-life reserve risk distribution Eric Dal Moro, Fellow of the French Actuarial Association Abstract: In the daily tasks of a non-life actuary, the reserve risk distribution plays a central role. For example, the estimation of the cost of capital used in commutation pricing relies heavily on the assumption retained for the shape of the non-life reserve risk distribution. Even though some distributions are widely used in the actuarial community (e.g. Lognormal distribution), it is interesting to note that very little is known on the determinants of the shape of the non-life reserve risk distribution. In general, the mean is usually defined as the Best Estimate and the standard deviation can be estimated using different methods (e.g. Mack 1993a). In terms of higher moments, Generalized Linear Models (GLM) and bootstrap techniques offer different possibilities of quantifying moments and quantiles (see Wüthrich-Merz 2008 and England and Verrall 2002). However, these models require the specification of some explicit parametric distribution (e.g. for the residuals) in order to be applied. Following a first introduction of skewness estimation of non-life reserve risk distribution (see Dal Moro 2012), this article investigates the possibility to estimate the kurtosis of the non-life reserve risk distribution. In addition, the robustness of the skewness and kurtosis estimation based on the proposed formulas is tested on eight different triangles