Sequential Monte Carlo Methods for Computing Probabilities of Rare Events in Complex Models

Abstract

It has been widely recognized that importance sampling provides a powerful tool for Monte Carlo evaluation of probabilities of rare events. This tool, however, has been hampered by difficulties in finding (or sampling from) the optimal proposal distribution and/or difficulties in evaluating the importance weights in complex statistical models. We show how these difficulties can be circumvented by using recent advances in sequential importance sampling with resampling. Applications to rare event simulation and percentile estimates in insurance mathematics and financial risk management, which involve serially dependent and high-dimensional data, are given. This is joint work with T.L. Lai.