Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Equivalence of Stochastic Optimal Control Problems with Open and
  Closed Loop Controls   For an optimal control problem of an It\^o's type stochastic differential
equation, the control process could be taken as open-loop or closed-loop forms.
In the standard literature, provided appropriate regularity, the value
functions under these two types of controls are equal and are the unique
(viscosity) solution to the corresponding (path-dependent) HJB equation. In
this short note, we provide a counterexample in the path dependent setting
showing that these value functions can be different in general.

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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol