Simulating ruin probabilities in insurance risk processes with subexponential claims

We describe a fast simulation framework for simulating small ruin probabilities in insurance risk processes with subexponential claims. Naive simulation is inefficient since the event of interest is rare, and special simulation techniques like importance sampling need to be used. An importance sampling change of measure known as sub-exponential twisting has been found useful for some rare event simulations in the subexponential context. We describe conditions that are sufficient to ensure that the infinite horizon probability can be estimated in a (work-normalized) large set asymptotically optimal manner, using this change of measure. These conditions are satisfied for some large classes of insurance risk processes - e.g., processes with Markov-modulated claim arrivals and claim sizes - where the heavy tails are of the 'Weibull type'. We also give much weaker conditions for the estimation of the finite horizon ruin probability. Finally, we present experiments supporting our results.