Rare‐Event Simulation

Abstract

This chapter describes algorithms for the efficient estimation of rare-event probabilities. It starts by defining the notion of efficiency in the context of rare-event simulation, and then considers the algorithms that are efficient in a particular rare-event setting. The algorithms are importance sampling for light tails, conditional Monte Carlo for the estimation of probabilities arising from compound sums of heavy-tailed random variables, state-dependent importance sampling for rare-event overflow probabilities, general importance sampling — such as the cross-entropy method — with applications to financial risk modeling, and splitting methods for estimation of hitting probabilities of Markov processes. Controlled Vocabulary Terms cross-entropy method; importance sampling; Markov process; Monte Carlo methods; probability measure