A Simulation Procedure for Comparing Different Claims Reserving Methods

The estimation of outstanding claims is one of the important aspects in the management of the insurance business. Various methods have been widely dealt with in the actuarial literature. Exploration of the inaccuracies involved is traditionally based on a post-facto comparison of the estimates against the actual outcomes of the settled claims. However, until recent years it has not been usual to consider the inaccuracies inherent in claims reserving in the context of more comprehensive (risk theoretical) models, the purpose of which is to analyze the insurer as a whole. Important parts of the technique which will be outlined in this paper can be incorporated into over-all risk theory models to introduce the uncertainty involved with technical reserves as one of the components in solvency and other analyses. The idea in this paper is to describe a procedure by which one can explore how various reserving methods react to fictitious variations, fluctuations, trends, etc. which might influence the claims process, and, what is most important, how they reflect on the variables indicating the financial position of the insurer. For this purpose, a claims process is first postulated and claims are simulated and ordered to correspond to an actual handling of the observed claims of a fictitious insurer. Next, the simulation program will ‘mime’ an actuary who is calculating the claims reserve on the basis of the reserved claims. The difference between reserved amounts and settled amounts gives the reserving (run-off) error in this particular simulated case. By repeating the simulation numerous times (Monte Carlo method) the distribution of the error can be estimated as well as its effect on the total outcome of the insurer. By varying the assumptions which control the claims process the sensitivity of the reserving method vis-à-vis the assumed phenomena can be tested. By applying the procedure to several reserving methods in parallel, a conception of their properties can be gained; in particular, how robust they are against various variations and irregularities in the claims process. After having first described our method in general terms a number of numerical examples will be given to illustrate some of its relevant features. They are based on some well-known elementary reserving rules and simple assumptions on the claims process. Also some conclusions on the properties of the reserving rules are derived there from.