Non-Poissonian claimsʹ arrivals and calculation of the probability of ruin

Collective risk model with a special emphasize on non-Poissonian claimsʹ arrival processes is considered. Exact and approximate techniques for the calculation of the probabilities of ruin are examined. Simulation going back to the importance sampling is applied to two particular cases of non-Poissonian claims arrival processes to illustrate strong dependence of the probabilities of ruin on the interclaims distribution.