Deep quantile and deep composite triplet regression

Tobias Fissler, Michael Merz and Mario V. Wüthrich

Insurance: Mathematics and Economics, 2023, vol. 109, issue C, 94-112

Abstract: A main difficulty in actuarial claim size modeling is that covariates may have different effects on the body of the conditional distribution and on its tail. 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). This allows us to simultaneously fit different regression models in the two different parts of the conditional distribution function. To facilitate M-estimation for such models, we introduce and characterize the class of strictly consistent scoring functions for the triplet consisting of 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 data set from accident insurance.

Keywords: Elicitability; Consistent loss function; Proper scoring rule; Bregman divergence; Quantile and expected shortfall regression; Conditional tail expectation; Neural network regression; Splicing model (search for similar items in EconPapers)
JEL-codes: C14 C31 C45 C51 C52 C58 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:109:y:2023:i:c:p:94-112

DOI: 10.1016/j.insmatheco.2023.01.001

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