Quotation Fissler, Tobias, Merz, Michael, Wüthrich, Mario V. 2021. Deep Quantile and Deep Composite Model Regression.




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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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Working/discussion paper, preprint
Language English
Title Deep Quantile and Deep Composite Model Regression
Year 2021
URL https://arxiv.org/abs/2112.03075
JEL C14; C31; C450; C510; C520; C580


Fissler, Tobias (Details)
Merz, Michael (University of Hamburg, Germany)
Wüthrich, Mario V. (ETH Zurich, Switzerland)
Institute for Statistics and Mathematics IN (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1117 Actuarial mathematics (Details)
1137 Financial mathematics (Details)
1139 Neuronal (neural) networks (Details)
1162 Statistics (Details)
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