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A BIFURCATION APPROACH FOR ATTRITIONAL AND LARGE LOSSES IN CHAIN LADDER CALCULATIONS

  • Ulrich Riegel (a1)

Abstract

We introduce a stochastic model for the development of attritional and large claims in long-tail lines of business and present a corresponding “chain ladder-like” IBNR method which allows the use of claims payment data for attritional and claims incurred data for large losses. We derive formulas for the mean squared error of prediction and apply the method to a German motor third party liability portfolio.

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[1]Braun, Ch. (2004) The prediction error of the chain ladder method applied to correlated run-off triangles. Astin Bulletin, 34 (2), 399423.
[2]Buchwalder, M., Bühlmann, H., Merz, M. and Wüthrich, M.V. (2006) The mean square error of prediction in the chain ladder reserving method (Mack and Murphy Revisited). Astin Bulletin, 36 (2), 521542.
[3]Dahms, R. (2012) Linear stochastic reserving methods. Astin Bulletin, 42 (1), 134.
[4]Klugman, S.A., Panjer, H.A. and Willmot, G.E. (2004) Loss Models: From Data to Decisions, 2nd ed.New York: Wiley.
[5]Mack, Th. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. Astin Bulletin, 23 (2), 213225.
[6]Mack, Th., Quarg, G. and Braun, Ch. (2006) The mean square error of prediction in the chain ladder reserving method – A comment. Astin Bulletin, 36 (2), 543552.
[7]Mack, Th. (2002) Schadenversicherungsmathematik, 2nd ed.Karlsruhe:Verlag Versicherungswirtschaft.
[8]Quarg, G. and Mack, Th. (2004) Munich chain ladder. Blätter der DGVFM, 26 (4), 597630.
[9]Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Chichester: John Wiley & Sons.

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A BIFURCATION APPROACH FOR ATTRITIONAL AND LARGE LOSSES IN CHAIN LADDER CALCULATIONS

  • Ulrich Riegel (a1)

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