Nahid Abbasi - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran
Kazem Nouri - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran

In this paper, we study the numerical calculation to obtain bounds for the nite time ruinprobabilities for two particular insurance risk models, that both models are extensions of theclassical risk model. The rst model allows for the investment at a xed rate of interest ofthe surplus whenever this is above a given level. The second model studied in this paper isthe classical risk model modi ed by allowing the rate of premium income to vary throughtime according to the level of the surplus. An essential feature of the two models studiedin this paper is that they are time-homogeneous Markov processes. Also we discuss the ex-tension of these models to allow for the parameters to change over time in a deterministic way.

Ruin probability, Risk models, Numerical algorithms, Markov chains