Hansjoerg Albrecher: Matrix Distributions and Insurance Risk Models

Hansjoerg Albrecher (Université de Lausanne): Matrix Distributions and Insurance Risk Models

In this talk some recent developments on matrix distributions and their connection to absorption times of inhomogeneous Markov processes will be discussed, in particular how and why such constructions are natural tools for modelling in non-life and life insurance applications. We illustrate the approach for the modelling of mortality in both a single- and multi-population context, as well as modelling of joint lifetimes of couples. Finally, it is shown how certain extensions to the non-Markovian case involve fractional calculus and lead to matrix Mittag-Leffler distributions, which turn out to be a flexible and parsimonious class for the modelling of large but rare insurance loss events.

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