Continuous chain-ladder with paid data |
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Authors: | Stephan M. Bischofberger Munir Hiabu Alex Isakson |
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Affiliation: | 1. Cass Business School, University of London, London, UK stephan.bischofberger@cass.city.ac.ukhttps://orcid.org/0000-0002-2751-7419;3. School of Mathematics and Statistics, University of Sydney, Sydney, Australia https://orcid.org/0000-0001-5846-667X;4. Cass Business School, University of London, London, UK |
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Abstract: | We introduce a continuous-time framework for the prediction of outstanding liabilities, in which chain-ladder development factors arise as a histogram estimator of a cost-weighted hazard function running in reversed development time. We use this formulation to show that under our assumptions on the individual data chain-ladder is consistent. Consistency is understood in the sense that both the number of observed claims grows to infinity and the level of aggregation tends to zero. We propose alternatives to chain-ladder development factors by replacing the histogram estimator with kernel smoothers and by estimating a cost-weighted density instead of a cost-weighted hazard. Finally, we provide a real-data example and a simulation study confirming the strengths of the proposed alternatives. |
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Keywords: | Chain-ladder method general insurance granular reserving nonparametric estimation survival analysis |
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