Discrete time reward processes, stochastic annuities and insurance models

Abstract. The Markov and semi-Markov reward processes are a very powerful tool. They can be applied in many different fields, like mechanical systems, evaluation of computer systems etc. But in authors’ opinion the most fruitful and natural application environment of these tools is the insurance field. In the paper will be given the definition of stochastic annuity and of its generalization their strict relation to the homogeneous and non-homogeneous semi-Markov reward processes. At last it will be shown how is natural to apply these rewards processes in the insurance environment.