Application and Bootstrapping of the Munich Chain Ladder Method

University essay from KTH/Matematisk statistik

Abstract:

Point estimates of the Standard Chain Ladder method (CLM) and of the more complex Munich Chain Ladder method (MCL) are compared to real data on 38 different datasets in order to evaluate if MCL produces better predictions on average with a dataset from an arbitrary insurance portfolio. MCL is also examined to determine if the future paid and incurred claims converge as time progresses. A bootstrap model based on MCL (BMCL) is examined in order to evaluate its possibility to estimate the probability density function (PDF) of future claims and observable claim development results (OCDR). The results show that the paid and incurred predictions by MCL converge. The results also show that when considering all datasets MCL produce on average better estimations than CLM with paid data but no improvement can be seen with incurred data. Further the results show that by considering a subset of datasets which fulfil certain criteria, or by only considering accident years after 1999 the percentage of datasets in which MCL produce superior estimations increases. When examining BMCL one finds that it can produce estimated PDFs of ultimate reserves and OCDRs, however the mean of estimate of ultimate reserves does not converge to the MCL estimates nor do the mean of the OCDRs converge to zero. In order to get the right convergence the estimated OCDR PDFs are centered and the mean of the BMCL estimated ultimate reserve is set to the MCL estimate by multiplication.

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