Ruin probabilities of the discrete-time risk model with inhomogeneous claims

In this thesis, the discrete-time risk model with inhomogeneous claims is investigated. This model describes an insurance company who experiences two opposing cash flows: incoming cash premiums and outgoing claims and also depends on initial surplus. The main risk measure of the model, ruin probability, is considered and recursive formulas for the ruin probabilities calculating are obtained. These formulas enable fast and accurate evaluation of the finite-time and ultimate ruin probabilities of the discrete-time risk model with inhomogeneous claims. The results are presented in 4 chapters. In the second chapter the recursive relations for the finite-time ruin probabilities calculating of the discrete-time any multi-risk model are obtained. In the third chapter the recursive relations for the ultimate ruin probabilities calculating of the discrete-time bi-risk model and risk model with three inhomogeneous claims are obtained. In the fourth chapter the recursive relations for the finite-time ruin probabilities calculating of the discrete-time three-seasonal risk model are obtained. In the fifth chapter numerical examples of the obtained recursive relations are presented. The thesis also contains an introduction, background on the techniques used, conclusions and bibliography. Additionally to the thesis, an extensive summary in Lithuanian is provided