The Skewness of Bornhuetter-Ferguson

The Bornhuetter-Ferguson method is among the more popular methods of projecting non-life paid or incurred triangles. For this method, Thomas Mack developed a stochastic model allowing the estimation of the prediction error resulting from such projections. Mack’s stochastic model involves a parametrization of the Bornhuetter-Ferguson method based on incremental triangles of incurred or paid. Hence, that parametrized method differs from how Bornhuetter-Ferguson is usually applied on cumulative triangles of incurred or paid. Based on that proposed stochastic model, this paper provides a first approach for the estimation of the third moment, i.e., the skewness, of the resulting reserving distribution. An estimate of the third moment is useful in the context of IFRS 17, which directs that the quantile corresponding to the addition of a risk margin on top of the best estimate must be disclosed. To illustrate the proposed method, a few numerical examples are provided.