Mathematisch-Naturwissenschaftliche Fakultät

Institut für Mathematik

Fachgebiet: Versicherungsmathematik

Betreuer: Prof. Dr. Hartmut Milbrodt

Dipl.-Math. Marko Helwich
(e-mail: )

Durational effects and non-smooth semi-Markov models in life insurance

In considering life insurance contracts, durational effects may appear at two levels. The first is concerned with the underlying biometrical risk, meaning that dependencies of transition probabilities on the previous duration in a certain state can be observed. An example is given by recovery rates of disabled insured which additionally depend on the time elapsed since disablement. Secondly, there is a need for duration-depending actuarial payments. Both of these durational effects cannot be explicitly implemented in the common model relying on Markovian pure jump processes. The model presented here, based on semi-Markov processes, allows one to directly model dependencies on the previous duration. Due to the generality of the approach, discrete and continuous life insurance models can be similarly discussed. Relying on real data, numerical examples dealing with disability insurance as well as German private health insurance outline the impact of using duration-depending transition rates.