Recent Development in Claims Reserving

This contribution deals with recent development in the field of mathematical loss reserving via Chain Ladder that is regarded as the most popular method for setting technical reserves in non life insurance. It could be formulated deterministically or via a stochastic model. However there are some drawbacks of using this method automatically that will be discussed. Its generalisation Munich Chain Ladder method will be introduced as a result of it. Finally we will present some further results of more detailed analysis of this method including type of estimates, elasticities of reserve depending on estimate and problems of variability calculation. Introduction Non life Insurance companies are obliged to set up technical reserves for not yet unpaid claims which occurred in the past calendar years. The respective delay until the claim is paid is caused by the time between the date of accident and the date of reports to the insurer and moreover it will take another more time to settle the claim. In order to give realistic financial picture of the overall volume of the claims two types of technical reserves are set up. RBNS reserve is set up for Reported But Not Settled claims and IBNR reserve deals with the problem of Incurred But Not Reported claims. The first one may be determined by individual estimates for each known not paid claim regarding the experiences and expert opinion of future compensation that is usually made by employee of claims department. The latter reserve could be determined only via mathematical methods using the known development of paid compensation and RBNS reserve. If RBNS reserve is not set up individually as estimate of future paid compensation for each and every claim, an actuary can use only data describing the development of paid compensation and estimate the sum of RBNS and IBNR reserves together. We will mark Yi,j, i = 0, . . . , n, j = 0, . . . , n − i for data of paid claim or incurred where n notifies the dimension of the data sets. It is assumed that there is no development if n periods after accident pass. If we want to distinguish type of triangle we will add upper indices Y P i,j for data of paid compensation or Y I i,j for incurred data (sum of paid compensation and corresponding value of RBNS reserve). These data are usually analysed in the so called run-off triangles which could be seen as a matrix where only data in the upper left triangle are known and our aim is to estimate the future development in the lower right triangle. Each row is interpreted as one accident period and each column as a development period (i.e. the variable Yi,j shows us overall paid or incurred value of all claims occurred in period i and paid or reported until j periods after the accident happened). Thus figures of each diagonal corresponds to one single calendar period. Standard Chain Ladder Method That is the most widely used method in loss reserving used for each single run-off triangle. It originates from intuitive deterministic assumptions which were later generalised to obtain stochastic model of chain ladder. Standard Chain Ladder deterministic approach This method is described in the actuarial monographs, e.g. [ it Cipra, 1999] or [ it Mandl, 1999] and is based on the assumption that ratios of following values in one raw are approximately WDS'06 Proceedings of Contributed Papers, Part I, 118–123, 2006. ISBN 80-86732-84-3 © MATFYZPRESS