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arXiv · 2406.03252

Continuous-time modeling and bootstrap for chain-ladder reserving

Nicolas Baradel
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Abstract

We revisit the famous Mack's model which gives an estimate for the conditional mean squared error of prediction of the chain-ladder claims reserves. We introduce a stochastic differential equation driven by a Brownian motion to model the accumulated total claims amount for the chain-ladder method. Within this continuous-time framework, we propose a bootstrap technique for estimating the distribution of claims reserves. It turns out that our approach leads to inherently capturing asymmetry and non-negativity, eliminating the necessity for additional assumptions. We conclude with a case study and comparative analysis against alternative methodologies based on Mack's model.

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Nicolas Baradel. 2024-06-05. Continuous-time modeling and bootstrap for chain-ladder reserving. https://doi.org/10.1016/j.insmatheco.2025.103176

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