Conjugate processes and the silumation of ruin problems

A general methods is developed for giving simulation estimates of boundary crossing probabilities for processes related to random walks in discreate or continuous time. Particular attention is given to the probability ψ(u, T of ruin before time T in cpumpound Poisson risk processes. When the provbabi;ity law P governing the given process is imbedded in an exponentaial family (P_gq), one can write ψ (u, T) + _θR_gq for certain random variables R_gq given by Wald's fundamental identity. Using this to simulate from P_gq 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 different is illustrated by two examples.