A general method is developed for giving simulation estimates of the probability ψ(u, T) of ruin before time T. When the probability law P governing the given risk reserve process is imbedded in an exponential family (Pθ), one can write ψ(u, T) = EθRθ for certain random variables Rθ given by the fundamental identity of sequential analysis. Using this to simulate from Pθ rather than P, it is possible not only to overcome the difficulties connected with the case T = ∞, but also to obtain a considerable variance reduction. It is shown that the solution of the Lundberg equation determines the asymptotically optimal value of θ in heavy traffic when T = ∞, and some results guidelining the choice of θ when T < ∞ are also given. The potential of the method in complex models is illustrated by two examples.