Modelling Claims Runoff Triangles with Two-dimensional Time Series

1. Introduction This paper deals with the problem of forecasting the claims runoff of ordinary insurance business. Insurance companies are faced with the problem of making adequate provision for notified claims, and claims which may occur, on policies which they write. They have to do this to the satisfaction of policyholders, shareholders and the regulatory bodies and it is thus important that a soundly-based method is used to establish claims reserves. It is also important that such a method should be easily understood and that underlying the method is a theoretical basis which is known to give satisfactory results. Therefore, we shall take the simplest method of calculating claims reserves as the starting point and build into this more sophisticated estimation and forecasting techniques, without losing sight of the original model.