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arXiv · 1105.0745

Weak Dynamic Programming for Generalized State Constraints

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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Bruno Bouchard, Marcel Nutz. 2011-05-04. Weak Dynamic Programming for Generalized State Constraints. https://doi.org/10.1137/110852942

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