Conjugate distributions and variance reduction in ruin probability simulation

Extract

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 (P_θ), one can write ψ(u, T) = E_θR_θ for certain random variables R_θ given by the fundamental identity of sequential analysis. Using this to simulate from P_θ 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.