Munich Chain Ladder - A reserving methods that reduces the gap between IBNR projections based on paid losses and IBNR projections based on incurred losses

The IBNR reserve for a portfolio is usually calculated on the basis of both the run-off triangle of paid losses and the run-off triangle of incurred losses, i.e. the sum of paid losses and case reserves. Often, the problem arises that the projection based on paid losses is far different than the projection based on incurred losses. Even worse, paid losses may yield a higher ultimate loss projection than incurred losses in one accident year, but in the next accident year, the situation may be entirely reversed, with incurred losses yielding the higher projection of the ultimate loss. This paper analyses this problem with regard to the chain ladder methods, using examples and generally valid equations, and describes a solution: the Munich chain ladder method. More precisely, the paper shows that between paid losses and incurred losses there are almost always correlations that are ignored in the usual procedure of making a separate chain ladder method, on the other hand, takes advantage of these correlations, transferring any conjunction of paid and incurred losses that occurred in the past into the projection for the future. This paper presents in detail the properties, theoretical bases and, not least, capability of the new method, using numerous graphs and a fully elaborated example.