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Importance Sampling for Backward SDEs

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2010

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Bender, Christian

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https://doi.org/10.1080/07362990903546405
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Stochastic Analysis and Applications. Taylor & Francis. 2010, 28(2), pp. 226-253. ISSN 0736-2994. eISSN 1532-9356. Available under: doi: 10.1080/07362990903546405

Zusammenfassung

In this article, we explain how the importance sampling technique can be generalized from simulating expectations to computing the initial value of backward stochastic differential equations (SDEs) with Lipschitz continuous driver. By means of a measure transformation we introduce a variance reduced version of the forward approximation scheme by Bender and Denk [4 ] for simulating backward SDEs. A fully implementable algorithm using the least-squares Monte Carlo approach is developed and its convergence is proved. The success of the generalized importance sampling is illustrated by numerical examples in the context of Asian option pricing under different interest rates for borrowing and lending.

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510 Mathematik

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ISO 690BENDER, Christian, Thilo MOSELER, 2010. Importance Sampling for Backward SDEs. In: Stochastic Analysis and Applications. Taylor & Francis. 2010, 28(2), pp. 226-253. ISSN 0736-2994. eISSN 1532-9356. Available under: doi: 10.1080/07362990903546405
BibTex
@article{Bender2010-02-10Impor-52717,
  year={2010},
  doi={10.1080/07362990903546405},
  title={Importance Sampling for Backward SDEs},
  number={2},
  volume={28},
  issn={0736-2994},
  journal={Stochastic Analysis and Applications},
  pages={226--253},
  author={Bender, Christian and Moseler, Thilo}
}
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