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Unbiased Simulation of Rare Events in Continuous Time

Author

Listed:
  • James Hodgson

    (University of Warwick)

  • Adam M. Johansen

    (University of Warwick
    The British Library)

  • Murray Pollock

    (Newcastle University
    The British Library)

Abstract

For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and $$\varepsilon$$ ε -strong simulation of diffusions, which can be used to almost surely constrain sample paths to a given tolerance, suggests one way to do this. We specify how such algorithms can be combined with the classical multilevel splitting method for rare event simulation. This provides unbiased estimations of the probability in question. We discuss the practical feasibility of the algorithm with reference to existing $$\varepsilon$$ ε -strong methods and provide proof-of-concept numerical examples.

Suggested Citation

  • James Hodgson & Adam M. Johansen & Murray Pollock, 2022. "Unbiased Simulation of Rare Events in Continuous Time," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2123-2148, September.
  • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09886-2
    DOI: 10.1007/s11009-021-09886-2
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    References listed on IDEAS

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    4. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin & Tim Zajic, 1999. "Multilevel Splitting for Estimating Rare Event Probabilities," Operations Research, INFORMS, vol. 47(4), pages 585-600, August.
    5. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
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