On the Statistical Estimation of Costs of Claims

For a number of reasons it is important for an insurance company to estimate the claims costs of a year within the different branches of non-life insurance as soon as possible after the end of the year. The claims cost of a year is hereby defined as the total cost, before taking reinsurance into account, of all claims generated by events that have occurred during the year. When the estimation has to be done, part of these claims will be reported and closed, others will be reported and still open, and the remaining ones will be incurred but not yet reported. The total cost of the claims is defined as the sum of all payments that have been made or will be made on account of the claims. Thus, in this definition no regard is paid to interest, i.e. no discount factors are applied to payments to be made in the future.Instead of considering a year, we could consider an arbitrary period of twelve consecutive months. The estimation problem is the same, and estimates of the claims costs of consecutive twelve months periods will allow a closer following up of trends and yield predictions for the present year.For estimates to be available quickly, it is necessary that the estimation procedure be founded on data that are available immediately at the end of the year or the latest twelve months period. This means a.o. that for the bulk of the open claims, individual estimates of reserves by claims adjusters are out of the question. In other words, the estimation procedure has to be basically of a statistical character. In addition, for continuous estimates to be produced it has to be well adapted to electronic data processing. Indata to the procedure have to be stored in the memories of the computer.