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Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems
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We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the canonical space of paths, one can check the required measurability conditions. This covers in particular the most classical controlled/stopped diffusion processes problems. Further, we study the approximation property of the optimal control problems by piecewise constant control problems. As a byproduct, we obtain an equivalence result of the strong, weak and relaxed formulations of the controlled/stopped diffusion processes problem.
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Cited by 1 Pith paper
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Risk-sensitive exit-time control for stochastic differential equations with path-dependent coefficients
The small-noise limit of path-dependent risk-sensitive exit-time control is a deterministic control problem with Cameron–Martin cost.
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