A stochastic approach to catastrophic risks

Road transportation of dangerous materials as well as pollution are considered as being catastrophic risks. In case the normal insurance models are applied to catastrophic risks, one of the basic assumptions, namely that the average surplus is a linear quantity in time, is certainly not satisfied. In more realistic situations, an average movement of the surplus is linear up to a certain time, where a drastic decrease in the surplus occurs, namely at the moment when the claims are paid out, then afterwards the surplus will show a linear trend again.

In the present contribution we describe the stochastic approach to this kind of situations, based on the same ideas as used in ‘A stochastic approach to insurance cycles’ by Goovaerts et al. ( 1992). The consequences for the probability of ruin at a specific point in time are also investigated as well as their relation to solvency margins.