Sebastian Calcetero-Vanegas, Andrei L. Badescu, X. Sheldon Lin
arXiv 5 Jul 2023 · Econometrics · publishedEuropean Actuarial Journal (2024) · 3 citations (OpenAlex)
arXiv:2307.10808 · PDF · DOI · OpenAlex · Extracted main text
Claim reserving primarily relies on macro-level models, with the Chain-Ladder method being the most widely adopted. These methods were heuristically developed without minimal statistical foundations, relying on oversimplified data assumptions and neglecting policyholder heterogeneity, often resulting in conservative reserve predictions. Micro-level reserving, utilizing stochastic modeling with granular information, can improve predictions but tends to involve less attractive and complex models for practitioners. This paper aims to strike a practical balance between aggregate and individual models by introducing a methodology that enables the Chain-Ladder method to incorporate individual information. We achieve this by proposing a novel framework, formulating the claim reserving problem within a population sampling context. We introduce a reserve estimator in a frequency and severity distribution-free manner that utilizes inverse probability weights (IPW) driven by individual information, akin to propensity scores. We demonstrate that the Chain-Ladder method emerges as a particular case of such an IPW estimator, thereby inheriting a statistically sound foundation based on population sampling theory that enables the use of granular information, and other extensions.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Martńez-Miranda, M. D., Nielsen, J. P., and Verrall, R (2012) Double chain ladder | 1.000 | 5 | 3 | 100% |
| 2 | Bender, A., Groll, A., and Scheipl, F (2018) A generalized additive model approach to time-to-event analysis | 0.737 | 3 | 3 | 67% |
| 3 | Engler, N. and Lindskog, F (2024) Mack’s estimator motivated by large exposure asymptotics in a compound poisson setting | 0.737 | 3 | 2 | 100% |
| 4 | Fung, T. C., Badescu, A. L., and Lin, X. S (2022) Fitting censored and truncated regression data using the mixture of experts models self | 0.737 | 3 | 2 | 100% |
| 5 | Mack, T (1999) The standard error of chain ladder reserve estimates: Recursive calculation and inclusion of a tail factor | 0.737 | 3 | 2 | 100% |
| 6 | Thompson, S. K (2012) Sampling | 0.693 | 7 | 1 | 100% |
| 7 | Ma, X. and Wang, J (2020) Robust inference using inverse probability weighting | 0.644 | 4 | 1 | 100% |
| 8 | Andersen, P. K., Ørnulf Borgan, Hjort, N. L., Arjas, E., Stene, J.,… (1985) Counting process models for life history data: A review [with discussion and reply] | 0.644 | 2 | 2 | 100% |
| 9 | Asmussen, S. and Steffensen, M (2020) Risk and Insurance | 0.644 | 2 | 2 | 100% |
| 10 | England, P. and Verrall, R (2002) Stochastic claims reserving in general insurance | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 62 scored citations.