In insurance and even more in reinsurance it occurs that about a risk you only know that it has suffered no losses in the past say seven years. Some of these risks are furthermore such particular or novel that there are no similar risks to infer the loss frequency from.
We propose a loss frequency estimator that copes with such situations, by just relying on the information coming from the risk itself: the “amended sample mean”. It is derived from a number of reasonable mathematical first principles and turns out to have desirable statistical properties.
Some variants are possible, which enables insurers to align the method to their preferred business strategy, by trading off between low initial premiums for new business and moderate premium increases for renewal business after a loss.
We further give examples where it is possible to assess also the average loss, from some market or portfolio information, such that overall one has an estimator of the risk premium.