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Weak Dynamic Programming for Generalized State Constraints

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  • Bruno Bouchard
  • Marcel Nutz
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    Abstract

    We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expectation constraints and prove a comparison theorem to obtain the equation for closed state constraints.

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    File URL: http://arxiv.org/pdf/1105.0745
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1105.0745.

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    Date of creation: May 2011
    Date of revision: Oct 2012
    Publication status: Published in SIAM Journal on Control and Optimization, Vol. 50, No. 6, pp. 3344-3373, 2012
    Handle: RePEc:arx:papers:1105.0745

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    Web page: http://arxiv.org/

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    Cited by:
    1. Gordan Zitkovic, 2013. "Dynamic Programming for controlled Markov families: abstractly and over Martingale Measures," Papers 1307.5163, arXiv.org, revised Mar 2014.
    2. Bruno Bouchard & Ludovic Moreau & Marcel Nutz, 2012. "Stochastic Target Games with Controlled Loss," Papers 1206.6325, arXiv.org, revised May 2013.
    3. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2013. "Hedging under an expected loss constraint with small transaction costs," Papers 1309.4916, arXiv.org.
    4. Adrien Nguyen Huu & Nadia Oudjane, 2014. "Hedging Expected Losses on Derivatives in Electricity Futures Markets," Papers 1401.8271, arXiv.org.
    5. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org.

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