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Unbiased simulation method with the poisson kernel method for stochastic differential equations with reflection

  • Tomooki YuasaEmail author
Original Paper
  • 4 Downloads

Abstract

We consider unbiased simulation methods for one-dimensional stochastic differential equations with reflection at zero. In particular, we propose improvements of the forward unbiased simulation method provided by Alfonsi et al. (Parametrix methods for one-dimensional reflected SDEs. Modern problems of stochastic analysis and statistics: selected contributions in honor of Valentin Konakov. Springer, pp 43–66, 2017). In this paper, we will apply the Poisson kernel method to improve the negativity and high variance problems of the associated simulation method. We also discuss some choices for the behavior of the approximation process near the boundary. This improvement is demonstrated through some numerical experiments.

Keywords

Unbiased simulation method Stochastic differential equations Parametrix method 

Mathematics Subject Classification

Primary 60H35 

Notes

Acknowledgements

The author would like to thank Arturo Kohatsu-Higa for his helpful comments, and was supported by JSPS Grant 17J05514.

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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesRitsumeikan UniversityKusatsuJapan

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