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Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations

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  • Gobet, E.
  • Turkedjiev, P.

Abstract

We design an importance sampling scheme for backward stochastic differential equations (BSDEs) that minimizes the conditional variance occurring in least-squares Monte-Carlo (LSMC) algorithms. The Radon–Nikodym derivative depends on the solution of BSDE, and therefore it is computed adaptively within the LSMC procedure. To allow robust error estimates w.r.t. the unknown change of measure, we properly randomize the initial value of the forward process. We introduce novel methods to analyze the error: firstly, we establish norm stability results due to the random initialization; secondly, we develop refined concentration-of-measure techniques to capture the variance reduction. Our theoretical results are supported by numerical experiments.

Suggested Citation

  • Gobet, E. & Turkedjiev, P., 2017. "Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1171-1203.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:4:p:1171-1203
    DOI: 10.1016/j.spa.2016.07.011
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    Cited by:

    1. Teng, Long, 2022. "Gradient boosting-based numerical methods for high-dimensional backward stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    2. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2021. "Stability of backward stochastic differential equations: the general case," Papers 2107.11048, arXiv.org, revised Apr 2023.

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