The Study of basic risk processes by discrete-time non-homogeneous Markov processes

This paper elaborates how it is possible to calculate precisely the aggregate claim amount and the claim number by means of Markov reward models in a non-homogeneous time setting. More precisely, evolution equations of the non-homogeneous Markov reward processes are presented in a discounted environment for the calculation of the aggregate claim amount and in a non-discounted case for the calculation of the claim number. The underlying Markov process has a denumerable number of states. In the last section, an application of the proposed models is presented using real data obtained by merging databases of two small insurance companies. The results highlight the importance of the insured's age in the calculation of the actuarial quantities.