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A GENERALIZED LOSS RATIO METHOD DEALING WITH UNCERTAIN VOLUME MEASURES
Published online by Cambridge University Press: 22 April 2018
Abstract
Unlike chain ladder, the loss ratio method requires volume measures. Typically, these volumes are assumed to be known. In practice, however, accurate volume measures are rarely available. We interpret the available volumes as estimators for the true volume measures and analyze the consequences for the loss ratio method. In particular, we calculate the mean squared error of prediction, including uncertainty of volume measures, and derive approximately optimal weights for the observed incremental loss ratios. We then introduce a generalization of the loss ratio method that is tailored to the situation of uncertain volume measures and calculate the prediction uncertainty of this generalized loss ratio method.
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- Copyright © Astin Bulletin 2018
References
ASTIN Working Party on Non-Life Reserving (2016) Non-life reserving practices report, http://www.actuaries.org.Google Scholar
Clark, D.R. (2008) Reserving with incomplete exposure information. CAS E-Forum, Fall 2008.Google Scholar
Gluck, S.M. (1997) Balancing development and trend in loss reserve analysis. Conference Paper, 1997 Annual Meeting of the Casualty Actuarial Society.Google Scholar
Gütschow, T., Hess, K.T. and Schmidt, K.D. (2017) Separation of small and large claims on the basis of collective models. Scandinavian Actuarial Journal, pp. 1–19. doi: 10.1080/03461238.2017.1394364Google Scholar
Hess, K.T., Schmidt, K.D. and Zocher, M. (2006) Multivariate loss prediction in the multivariate additive model. Insurance Mathematics and Economics, 39, 185–191.Google Scholar
Härdle, W.K. and Hlávka, Z. (2007) Multivariate Statistics: Exercises and Solutions. New York: Springer.Google Scholar
Kaas, R., Goovaerts, M., Dhaene, J. and Denuit, M. (2001) Modern Actuarial Risk Theory. Boston: Kluwer Academic Publishers.Google Scholar
Korn, U. (2016) An extension to the Cape Cod method with credibility weighted smoothing. CAS E-Forum, Summer 2016.Google Scholar
Merz, M. and Wüthrich, M. V. (2009) Prediction error of the multivariate additive loss reserving method of dependent lines of business. Variance, 3, 131–151.Google Scholar
Riegel, U. (2014) A bifurcation approach for attritional and large losses in chain ladder calculations. ASTIN Bulletin, 44 (1), 127–172.Google Scholar
Riegel, U. (2015) A quantitative study of chain ladder based pricing approaches for long-tail quota shares. ASTIN Bulletin, 45 (2), 267–307.Google Scholar
Riegel, U. (2016) Bifurcation of attritional and large losses in an additive IBNR environment. Scandinavian Actuarial Journal, 2016 (7), 604–623.CrossRefGoogle Scholar
Saluz, A., Bühlmann, H., Gisler, A. and Moriconi, F. (2014) Bornhuetter-Ferguson Reserving Method with Repricing. Available at SSRN: https://ssrn.com/abstract=2697167Google Scholar
Saluz, A., Gisler, A. and Wüthrich, M.V. (2011) Development pattern and prediction error for the stochastic Bornhuetter–Ferguson claims reserving method. ASTIN Bulletin, 41 (2), 279–313.Google Scholar