In this paper motor liability insurance is considered from the viewpoint of an excess of loss reinsurer.

The reinsurer pays portions of claim amounts in excess of a contractually agreed limit, further referred to as excess point.

Aspects of practical interest are the rating of new contracts and cost-projections on claims occurred in past years which have not yet been reported.

What causes a major difficulty to a rating approach is the timelag between the occurrence of a claim and its settlement.

During this timelag, which may extend to ten years or even longer, the size of a claim will usually increase considerably. This is due to such factors as inflation and more victim oriented legal procedures.

As a result of this phenomenon, a claim, initially not involving the reinsurer, may confront him many years later, when its size overtakes the excess point. Hence, each risk year produces a generation of claims stretching far into the future.

The problem facing the reinsurer trying to compute premiums is that he must look, say ten years into the future, on the basis of incomplete data.

The table below is a schematic presentation of the time history of a contract that started k years ago.

The experience is assumed to be expressed in numbers of claims exceeding a constant excess point.

Successive rows show the generations of excess claims down to the last completed risk year k.

In the pages that follow we will attempt to project expected numbers of excess claims into the future, using information as schematized in this table.