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Importance sampling for McKean-Vlasov SDEs

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  • dos Reis, Gonçalo
  • Smith, Greig
  • Tankov, Peter

Abstract

This paper deals with Monte-Carlo (MC) methods for evaluating expectations of functionals of solutions to McKean-Vlasov Stochastic Differential Equations (MV-SDE) including those with super-linearly growing drifts. Underpinned by an interacting particle system approximation, we propose two importance sampling (IS) algorithms to reduce the variance of an associated MC estimator.

Suggested Citation

  • dos Reis, Gonçalo & Smith, Greig & Tankov, Peter, 2023. "Importance sampling for McKean-Vlasov SDEs," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    • Handle: RePEc:eee:apmaco:v:453:y:2023:i:c:s0096300323002473
    DOI: 10.1016/j.amc.2023.128078
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    References listed on IDEAS

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    1. Huei-Wen Teng & Cheng-Der Fuh & Chun-Chieh Chen, 2016. "On an automatic and optimal importance sampling approach with applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1259-1271, August.
    2. Genin, Adrien & Tankov, Peter, 2020. "Optimal importance sampling for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 20-46.
    3. Paolo Guasoni & Scott Robertson, 2008. "Optimal importance sampling with explicit formulas in continuous time," Finance and Stochastics, Springer, vol. 12(1), pages 1-19, January.
    4. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152, April.
    5. Robertson, Scott, 2010. "Sample path Large Deviations and optimal importance sampling for stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 66-83, January.
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