Tobias Fissler, Michael Merz, Mario V. Wüthrich
arXiv 6 Dec 2021 · Statistics — Methodology
arXiv:2112.03075 · PDF · DOI · OpenAlex · Extracted main text
A main difficulty in actuarial claim size modeling is that there is no simple off-the-shelf distribution that simultaneously provides a good distributional model for the main body and the tail of the data. In particular, covariates may have different effects for small and for large claim sizes. To cope with this problem, we introduce a deep composite regression model whose splicing point is given in terms of a quantile of the conditional claim size distribution rather than a constant. To facilitate M-estimation for such models, we introduce and characterize the class of strictly consistent scoring functions for the triplet consisting a quantile, as well as the lower and upper expected shortfall beyond that quantile. In a second step, this elicitability result is applied to fit deep neural network regression models. We demonstrate the applicability of our approach and its superiority over classical approaches on a real accident insurance data set.
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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 | Dimitriadis, T., Fissler, T., Ziegel, J.F (2020) The efficiency gap self | 0.956 | 8 | 4 | 88% |
| 2 | Gneiting, T (2011) Making and evaluating point forecasts | 0.874 | 12 | 2 | 100% |
| 3 | Wüthrich, M.V., Merz, M (2021) Statistical foundations of actuarial learning and its applications self | 0.874 | 7 | 2 | 100% |
| 4 | Richman, R (2021) Mind the gap – safely incorporating deep learning models into the actuarial toolkit | 0.874 | 5 | 2 | 100% |
| 5 | Fissler, T., Ziegel, J.F (2016) Higher order elicitability and Osband's principle self | 0.843 | 10 | 3 | 60% |
| 6 | Koenker, R., Bassett, G., Jr (1978) Regression quantiles | 0.843 | 3 | 3 | 100% |
| 7 | Gneiting, T., Raftery, A.E (2007) Strictly proper scoring rules, prediction, and estimation | 0.737 | 3 | 2 | 100% |
| 8 | Fissler, T., Ziegel, J.F (2021) On the elicitability of range value at risk self | 0.644 | 3 | 2 | 67% |
| 9 | Guillen, M., Bermúdez, L., Pitarque, A (2021) Joint generalized quantile and conditional tail expectation for insurance risk analysis | 0.585 | 3 | 1 | 100% |
| 10 | Osband, K.H (1985) Providing Incentives for Better Cost Forecasting | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 39 scored citations.