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Importance Sampling and Stratification for Copula Models

  • Philipp Arbenz
  • Mathieu Cambou
  • Marius Hofert
  • Christiane LemieuxEmail author
  • Yoshihiro Taniguchi
Chapter

Abstract

An importance sampling approach for sampling from copula models is introduced. The proposed algorithm improves Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at least one of its components is large. Such problems often arise from dependence models in finance and insurance. The importance sampling framework we propose is particularly easy to implement for Archimedean copulas. We also show how the proposal distribution of our algorithm can be optimized by making a connection with stratified sampling. In a case study inspired by a typical insurance application, we obtain variance reduction factors sometimes larger than 1000 in comparison to standard Monte Carlo estimators when both importance sampling and quasi-Monte Carlo methods are used.

Notes

Acknowledgements

We thank the anonymous referees for their helpful comments. The third and fourth author gratefully acknowledge the financial support of NSERC Canada through grant numbers #5010 and #238959, respectively.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Philipp Arbenz
    • 1
    • 2
  • Mathieu Cambou
    • 3
  • Marius Hofert
    • 4
  • Christiane Lemieux
    • 4
    Email author
  • Yoshihiro Taniguchi
    • 4
  1. 1.SCORZurichSwitzerland
  2. 2.ETH ZurichZurichSwitzerland
  3. 3.EdgeLabLausanneSwitzerland
  4. 4.University of WaterlooWaterlooCanada

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