Abstract
The optimal control problem governed by the stochastic reflection problem associated with a closed convex set $K$ in $\mathbb{R}^d$ is reduced via the corresponding Kolmogorov equation to a deterministic bilinear parabolic optimal control problem on $(0,T)\times K$. In this way, one gets directly a stochastic optimal feedback controller by avoiding the standard dynamic programming equation associated with the stochastic optimal control problem.
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