Stochastic Simulation of Rare Events

Abstract

Stochastic simulation is an important and practical technique for computing probabilities of rare events, like the payoff probability of a financial option, the probability that a queue exceeds a certain level, or the probability of ruin of the insurer's risk process. Rare events occur so infrequently, that they cannot be reasonably recorded during a standard simulation procedure: specific simulation algorithms that thwart the rarity of the event to simulate are required. An important algorithm in this context is based on changing the sampling distribution and it is called importance sampling . Optimal Monte Carlo algorithms for computing rare event probabilities are either logarithmic efficient or possess bounded relative error.