Deep Quantile and Deep Composite Model Regression

TL;DR

This paper introduces a deep composite regression model for actuarial claim size data that adaptively models both the main distribution and tail effects using quantile-based splicing, improving fit over traditional methods.

Contribution

It proposes a novel deep composite regression framework with quantile-based splicing and develops consistent scoring functions for robust estimation, enhancing tail modeling in claim size data.

Findings

Outperforms classical models on real insurance data

Effectively captures tail behavior and covariate effects

Provides a new approach for flexible distributional modeling

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.