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Back-Testing the ODP Bootstrap of the Paid Chain- Ladder Model with Actual Historical Claims Data

This paper will back-test the popular over-dispersed Poisson (ODP) bootstrap of the paid chain-ladder model, as detailed in England and Verrall (2002), using real data from hundreds of U.S. companies, spanning three decades. The results show that this model produces distributions that underestimate reserve risk. Therefore, we propose two methods to increase the variability of the distribution so that it passes the back-test. In the first method, a set of benchmark systemic risk distributions are estimated by line of business that increase the variability of the bootstrapped distribution. In the second method, we show how one can apply a Wang Transform to estimate the systemic bias of the chain-ladder method over the course of the underwriting cycle.