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Continuous-time modeling and bootstrap for chain-ladder reserving

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  • Baradel, Nicolas

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.

Suggested Citation

  • Baradel, Nicolas, 2026. "Continuous-time modeling and bootstrap for chain-ladder reserving," Insurance: Mathematics and Economics, Elsevier, vol. 126(C).
    • Handle: RePEc:eee:insuma:v:126:y:2026:i:c:s0167668725001234
    DOI: 10.1016/j.insmatheco.2025.103176
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