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This work introduces an application of an semi-markov modell for the personal insurance. This is accomplished by presenting a way to compute the acturial reserve. The first part of this thesis reviews the markov and the semi-markov processes. Afterwards a semi markov process is used to establish a model for a genereal personal insurance. This model is then implemented in the programming language R as an surviving dependent pension and as a disability pension. Finally, the acturial reserve isdoi:10.34726/hss.2021.75660 fatcat:p2t7usqa2jcs7oaqebmmzsmvty