Soft splicing model: bridging the gap between composite model and finite mixture model

Considerations of both the heavy-tail phenomenon and multi-modality of a claim severity distribution have been challenging in the actuarial literature and practices. In this article, we develop a novel class of soft splicing models that bridges the gap between pre-existing methods for handling the issues above. The proposed method is flexible enough to incorporate tail-heaviness and multi-modality with computational efficiency and nests finite mixture models and splicing models as its special and/or limiting cases. The soft splicing model is also more robust in extrapolating the tail-heaviness of distribution subject to model contamination. According to simulation studies and real insurance claim data analyses, it is shown that the proposed soft splicing model provides superior goodness-of-fit and more accurate estimates of tail risk measures than both finite mixture and composite models.