By adding the information of reported count data to a classical triangle of reserving data, we derive a suprisingly simple method for forecasting IBNR and RBNS claims. A simple relationship between development factors allows to involve and then estimate the reporting and payment delay. Bootstrap methods provide prediction errors and make possible the inference about IBNR and RBNS claims, separately.

A claims reserving method is reviewed which was introduced by Gunnar Benktander in 1976. It is a very intuitive credibility mixture of Bornhuetter/Ferguson and Chain Ladder. In this paper, the mean squared errors of all 3 methods are calculated and compared on the basis of a very simple stochastic model. The Benktander method is found to have almost always a smaller mean squared error than the other two methods and to be almost as precise as an exact Bayesian procedure.

A fully time-continuous approach is taken to the problem of predicting the total liability of a non-life insurance company. Claims are assumed to be generated by a non-homogeneous marked Poisson process, the marks representing the developments of the individual claims. A first basic result is that the total claim amount follows a generalized Poisson distribution. Fixing the time of consideration, the claims are categorized into settled, reported but not settled, incurred but not reported, and covered but not incurred. It is proved that these four categories of claims can be viewed as arising from independent marked Poisson processes. By use of this decomposition result predictors are constructed for all categories of outstanding claims. The claims process may depend on observable as well as unobservable risk characteristics, which may change in the course of time, possibly in a random manner. Special attention is given to the case where the claim intensity per risk unit is a stationary stochastic process. A theory of continuous linear prediction is instrumental.