Conditional least squares and copulae in claims reserving for a single line of business |
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| Institution: | 1. Charles University in Prague, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Sokolovská 83, CZ-18675 Prague, Czech Republic;2. Humboldt University of Berlin, School of Business and Economics, Ladislaus von Bortkiewicz Chair of Statistics, C.A.S.E. –Center for Applied Statistics and Economics, Spandauer Strasse 1, D-10178 Berlin, Germany;1. School of Risk and Actuarial Studies, University of New South Wales, Sydney, Australia;2. CEPAR, Australia;1. School of Mathematics and Statistics, Southwest University, 400715 Chongqing, China;2. Department of Actuarial Science, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland;1. Department of Mathematics, Towson University, Towson, MD 21252, USA;2. Department of Bioinformatics & Biostatistics, University of Louisville, Louisville, KY, 40202, USA;1. Coöperatie Dela, P.O. Box 522, 5600 AM Eindhoven, The Netherlands;2. CentER and Netspar, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands;1. Faculty of Business and Economics (HEC Lausanne), University of Lausanne, 1015 Lausanne, Switzerland;2. School of Mathematics and Statistics, Southwest University, 400715 Chongqing, China |
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| Abstract: | One of the main goals in non-life insurance is to estimate the claims reserve distribution. A generalized time series model, that allows for modeling the conditional mean and variance of the claim amounts, is proposed for the claims development. On contrary to the classical stochastic reserving techniques, the number of model parameters does not depend on the number of development periods, which leads to a more precise forecasting.Moreover, the time series innovations for the consecutive claims are not considered to be independent anymore. Conditional least squares are used to estimate model parameters and consistency of these estimates is proved. The copula approach is used for modeling the dependence structure, which improves the precision of the reserve distribution estimate as well.Real data examples are provided as an illustration of the potential benefits of the presented approach. |
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| Keywords: | Claims reserving Reserve distribution Dependency modeling Copula Conditional least squares |
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