10. Rare-Event Simulation

  1. Dirk P. Kroese1,
  2. Thomas Taimre1 and
  3. Zdravko I. Botev2

Published Online: 20 SEP 2011

DOI: 10.1002/9781118014967.ch10

Handbook of Monte Carlo Methods

Handbook of Monte Carlo Methods

How to Cite

Kroese, D. P., Taimre, T. and Botev, Z. I. (2011) Rare-Event Simulation, in Handbook of Monte Carlo Methods, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118014967.ch10

Author Information

  1. 1

    University of Queensland

  2. 2

    Université de Montréal

Publication History

  1. Published Online: 20 SEP 2011
  2. Published Print: 28 FEB 2011

ISBN Information

Print ISBN: 9780470177938

Online ISBN: 9781118014967



  • conditional Monte Carlo;
  • cross-entropy method;
  • importance sampling;
  • Markov process;
  • probability estimation;
  • rare-event simulation;
  • splitting methods;
  • state-dependent importance sampling


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