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Backward stochastic differential equations with singular terminal condition

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  • Popier, A.

Abstract

In this paper, we are concerned with backward stochastic differential equations (BSDE for short) of the following type: where q is a positive constant and [xi] is a random variable such that . We study the link between these BSDE and the associated Cauchy problem with terminal data g, where g=+[infinity] on a set of positive Lebesgue measure.

Suggested Citation

  • Popier, A., 2006. "Backward stochastic differential equations with singular terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 2014-2056, December.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:12:p:2014-2056
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    References listed on IDEAS

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    1. 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.
    2. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    3. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
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    Citations

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    Cited by:

    1. Graewe, Paulwin & Horst, Ulrich & Séré, Eric, 2018. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 979-1006.
    2. Graewe, Paulwin & Popier, Alexandre, 2021. "Asymptotic approach for backward stochastic differential equation with singular terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 247-277.
    3. Matoussi, A. & Piozin, L. & Popier, A., 2017. "Stochastic partial differential equations with singular terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 831-876.
    4. Paulwin Graewe & Ulrich Horst & Eric S'er'e, 2013. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Papers 1309.0474, arXiv.org, revised Jun 2017.
    5. T Kruse & A Popier, 2015. "Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting," Papers 1504.01150, arXiv.org, revised Dec 2015.
    6. Ulrich Horst & Xiaonyu Xia & Chao Zhou, 2019. "Portfolio liquidation under factor uncertainty," Papers 1909.00748, arXiv.org.
    7. Kruse, T. & Popier, A., 2016. "Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2554-2592.
    8. Ulrich Horst & Xiaonyu Xia, 2018. "Continuous viscosity solutions to linear-quadratic stochastic control problems with singular terminal state constraint," Papers 1809.01972, arXiv.org, revised Apr 2020.
    9. T Kruse & A Popier, 2015. "Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting," Working Papers hal-01139364, HAL.
    10. Stefan Ankirchner & Alexander Fromm & Thomas Kruse & Alexandre Popier, 2018. "Optimal position targeting via decoupling fields," Working Papers hal-01500311, HAL.

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