Markov models with phase-type distributions in life insurance

Specialeforsvar ved Mikkel Møller-Larsen

Titel: Markov models with phase-type  distributions in life insurance

Abstract: This thesis studies phase-type distributions which are defined as Markov chains And Markov jump processes. Discrete phase-type distributions are defined as Markov chains and correspondingly phase-type distributions are defined as Markov jump processes. We discuss the strength and weaknesses for phase-type distributions, especially the weakness that they need to be time homogeneous in order for the phase-type distribution results to be valid. Therefore, we derive new results such that we extend the phase-type distributions results to inhomogeneous phase-type distributions both in discrete time and continuous time. For a discrete phase-type distribution the new derived results can handle any time inhomogeneity, while the new extensions in continuous time only are valid for phase-type distributions with piecewise constant transition intensities. These new results are implemented in a life insurance context, since we can find the phase-type distributions for the Markov models used in life insurance hence use the use the phase-type distributions theory. In discrete time we derive a formula for the prospective reserve for payments depending on a Markov chain. Further we also derive a discrete time version of Thiele’s differential equation.

Vejleder:  Mogens Bladt
Censor:    Søren Asmussen, Aarhus Universitet