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Weak Dynamic Programming for Generalized State Constraints

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  • Bruno Bouchard
  • Marcel Nutz

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.

Suggested Citation

  • Bruno Bouchard & Marcel Nutz, 2011. "Weak Dynamic Programming for Generalized State Constraints," Papers 1105.0745, arXiv.org, revised Oct 2012.
    • Handle: RePEc:arx:papers:1105.0745
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    File URL: https://arxiv.org/pdf/1105.0745
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