Weak Dynamic Programming for Generalized State Constraints

Bruno Bouchard and 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.

Date: 2011-05, Revised 2012-10
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Published in SIAM Journal on Control and Optimization, Vol. 50, No. 6, pp. 3344-3373, 2012

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1105.0745

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