Department seminar by Martin Bladt

Please Note: This seminar will be given online.

Matrix regression: models, algorithms, and applications

The task of modeling claim severities is addressed when data is not consistent with the classical regression assumptions. This framework is common in several lines of business within insurance and reinsurance, where catastrophic losses or heterogeneous sub-populations result in data difficult to model. Their correct analysis is required for pricing insurance products, and more generally, for risk management. In this talk, we propose to use regression models based on phase-type distributions. We first investigate regressing on the underlying inhomogeneous Markov intensity, generalizing the proportional hazards model. We subsequently show how variants of these models can be successfully applied to both loss and mortality modeling. The latter has the multi-state setting as a natural framework for describing the aging process. Finally, we introduce a model where covariates act on the initial probabilities of the underlying chain, which play the role of expert weights. The basic properties of such models are computed in terms of matrix functionals, and denseness properties are derived, demonstrating their flexibility. Effective estimation strategies are proposed, mainly based on the EM algorithm and weighted multinomial logistic regression models, and we provide illustrations using real-world datasets.