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Gaussian density estimates for solutions of fully coupled forward‐backward SDEs

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  • Christian Olivera
  • Evelina Shamarova

Abstract

We obtain upper and lower Gaussian density estimates for the laws of each component of the solution to a one‐dimensional fully coupled forward‐backward SDE. Our approach relies on the link between FBSDEs and quasilinear parabolic PDEs, and is fully based on the use of classical results on PDEs rather than on manipulation of FBSDEs, compared to other papers on this topic. This essentially simplifies the analysis.

Suggested Citation

  • Christian Olivera & Evelina Shamarova, 2020. "Gaussian density estimates for solutions of fully coupled forward‐backward SDEs," Mathematische Nachrichten, Wiley Blackwell, vol. 293(8), pages 1554-1564, August.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:8:p:1554-1564
    DOI: 10.1002/mana.201800381
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    References listed on IDEAS

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    1. Jérôme Detemple & René Garcia & Marcel Rindisbacher, 2005. "Representation formulas for Malliavin derivatives of diffusion processes," Finance and Stochastics, Springer, vol. 9(3), pages 349-367, July.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
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