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Weak Dynamic Programming for Generalized State Constraints

By Bruno Bouchard and 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.Comment: 36 pages;forthcoming in 'SIAM Journal on Control and Optimization

Topics: Mathematics - Optimization and Control, Computer Science - Systems and Control, Mathematics - Analysis of PDEs, Mathematics - Probability, Quantitative Finance - Risk Management, 93E20, 49L20, 49L25, 35K55
Year: 2012
DOI identifier: 10.1137/110852942
OAI identifier: oai:arXiv.org:1105.0745
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