Simulating the ruin probability of risk processes with delay in claim settlement

A risk process with delay in claim settlement is usually described in terms of a Poisson shot-noise process (see Klüppelberg and Mikosch (Bernoulli 1 (1995) 125) and Brémaud (Appl. Probab. 37 (2000) 914)). In particular, proves that under suitable conditions the corresponding ruin probability goes to zero not slower than an exponential rate. This yields problems if we want to estimate the ruin probability by a Monte Carlo simulation. In this paper we overcome these difficulties deriving the asymptotically efficient simulation law.