Phase-type distributions for claim severity regression modeling

TL;DR

This paper introduces phase-type distribution-based regression models for claim severity analysis, effectively capturing complex loss distributions with heavy tails and multimodality in insurance data.

Contribution

It proposes a novel regression framework using phase-type distributions with an EM algorithm extension, enhancing interpretability and flexibility over traditional models.

Findings

Models effectively capture heavy-tailed and multimodal distributions.

Regression framework generalizes proportional hazards models.

Demonstrates improved fit for insurance claim severity data.

Abstract

This paper addresses the task of modeling severity losses using segmentation when the data distribution does not fall into the usual regression frameworks. This situation is not uncommon in lines of business such as third-party liability insurance, where heavy-tails and multimodality often hamper a direct statistical analysis. We propose to use regression models based on phase-type distributions, regressing on their underlying inhomogeneous Markov intensity and using an extension of the EM algorithm. These models are interpretable and tractable in terms of multi-state processes and generalize the proportional hazards specification when the dimension of the state space is larger than one. We show that the combination of matrix parameters, inhomogeneity transforms, and covariate information provides flexible regression models that effectively capture the entire distribution of loss severities.