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A control problem with fuel constraint and Dawson-Watanabe superprocesses

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  • Alexander Schied

Abstract

We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of $J$-functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develop sharp bounds on the blow-up behavior of log-Laplace functionals of $J$-functionals, which might be of independent interest.

Suggested Citation

  • Alexander Schied, 2012. "A control problem with fuel constraint and Dawson-Watanabe superprocesses," Papers 1207.5809, arXiv.org, revised Dec 2013.
  • Handle: RePEc:arx:papers:1207.5809
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    File URL: http://arxiv.org/pdf/1207.5809
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    Cited by:

    1. Eyal Neuman & Alexander Schied, 2016. "Optimal portfolio liquidation in target zone models and catalytic superprocesses," Finance and Stochastics, Springer, vol. 20(2), pages 495-509, April.
    2. 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.
    3. T Kruse & A Popier, 2015. "Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting," Working Papers hal-01139364, HAL.
    4. Paulwin Graewe & Ulrich Horst, 2016. "Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience," Papers 1611.03435, arXiv.org, revised Jul 2017.
    5. 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.
    6. Charles-Albert Lehalle & Eyal Neuman, 2017. "Incorporating Signals into Optimal Trading," Papers 1704.00847, arXiv.org, revised Apr 2017.
    7. Hans Follmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.
    8. 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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