Analisis of Ruin Trobability for Insurance Companies using Markov chain

In this reserch, we show that the delayed Sparre Andersen insurance risk model can be analyzed as a Markov chain and we will use it for calculate the ruin probability for insurance companies. Then we describe how matrix analytic methods can be used to establish a computational procedure for calculating the probability distributions associated with fundamental ruin related quantities of interest such as the time of ruin the surplus immediately before ruin and deficit at ruin. Our aim in this research is more computational in flavour. At the beginning, we will show how the delayed Sparre Andersen model can be set up as a doubly infinite Markov chain. After this definitions we wil use this model for our calculations and at the end we calculate ruin probability for one of the Iranian insurance companies by using this model.