Deep Quantile and Deep Composite Model Regression

Understand

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.