Three Methods to Calculate the Probability of Ruin

The first method, essentmlly due to GOOVAERTS and DE VYLDER, uses the connection between the probablhty of ruin and the maximal aggregate loss random variable, and the fact that the latter has a compound geometric d lsmbutlon. For the second method, the claim amount distribution is supposed to be a combination of exponential or translated exponential distributions. Then the probablhty of rum can be calculated in a transparent fashmn; the mare problem is to determine the nontrlvlal roots of the equation that defines the adjustment coefficmnt. For the third method one observes that the probabihty of ruin is related to the stationary distribution of a certain associated process Thus it can be determined by a single simulation of the latter. For the second and third methods the assumption of only proper (positive) claims is not needed