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BSDEs with singular terminal condition and control problems with constraints

Author

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  • Stefan Ankirchner
  • Monique Jeanblanc
  • Thomas Kruse

Abstract

We provide a probabilistic solution of a not necessarily Markovian control problem with a state constraint by means of a Backward Stochastic Differential Equation (BSDE). The novelty of our solution approach is that the BSDE possesses a singular terminal condition. We prove that a solution of the BSDE exists, thus partly generalizing existence results obtained by Popier in [7] and [8]. We perform a verification and discuss special cases for which the control problem has explicit solutions.

Suggested Citation

  • Stefan Ankirchner & Monique Jeanblanc & Thomas Kruse, 2013. "BSDEs with singular terminal condition and control problems with constraints," Papers 1305.6541, arXiv.org, revised Jun 2013.
    • Handle: RePEc:arx:papers:1305.6541
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    File URL: https://arxiv.org/pdf/1305.6541
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    References listed on IDEAS

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    1. Popier, A., 2006. "Backward stochastic differential equations with singular terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 2014-2056, December.
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    Cited by:

    1. Paulwin Graewe & Ulrich Horst & Jinniao Qiu, 2013. "A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions," Papers 1309.0461, arXiv.org, revised Jan 2015.
    2. 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.
    3. Ulrich Horst & Jinniao Qiu & Qi Zhang, 2014. "A Constrained Control Problem with Degenerate Coefficients and Degenerate Backward SPDEs with Singular Terminal Condition," Papers 1407.0108, arXiv.org, revised Jul 2015.

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