Deep Quantile and Deep Composite Model Regression

Tobias Fissler, Michael Merz and Mario V. W\"uthrich

Papers from arXiv.org

Abstract: 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.

Date: 2021-12
New Economics Papers: this item is included in nep-big, nep-ecm, nep-ias and nep-rmg
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Citations: View citations in EconPapers (3)

Published in Insurance: Mathematics and Economics, 2023, Volume 109

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2112.03075

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