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BSDEs with singular terminal condition and control problems with constraints


  • Stefan Ankirchner
  • Monique Jeanblanc
  • Thomas Kruse


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.

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  • Stefan Ankirchner & Monique Jeanblanc & Thomas Kruse, 2013. "BSDEs with singular terminal condition and control problems with constraints," Papers 1305.6541,, revised Jun 2013.
  • Handle: RePEc:arx:papers:1305.6541

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    References listed on IDEAS

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    Cited by:

    1. 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,, revised Jul 2015.

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