Marcus Christiansen: Life insurance calculations in a non-Markovian world

Abstract

The life insurance literature focusses almost exclusively on Markov modeling and variants thereof, such as semi-Markov modeling. The talk reviews possible alternatives when Markov assumptions cannot be verified empirically. First, we discuss a full-information model that avoids information restrictions of Markov-type and fully retains possible path dependencies. We show that various classical risk-management techniques still work here, but the statistical and numerical challenges are huge due to model complexity. Second, we look at as-if-Markov modelling, which uses information restrictions of Markov-type but without actually making a Markov assumption. This reduces complexity and can build on recent progress from the survival analysis literature. A challenge is here the non-monotony of the information dynamics, which is a problem that is in fact not entirely new in the classical life insurance literature but got little attention so far. All in all, the talk reviews a number of concepts for moving beyond Markovian modelling and explains their possibilities and limitations.