Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic programming for optimal control of stochastic McKean-Vlasov
  dynamics   We study the optimal control of general stochastic McKean-Vlasov equation.
Such problem is motivated originally from the asymptotic formulation of
cooperative equilibrium for a large population of particles (players) in
mean-field interaction under common noise. Our first main result is to state a
dynamic programming principle for the value function in the Wasserstein space
of probability measures, which is proved from a flow property of the
conditional law of the controlled state process. Next, by relying on the notion
of differentiability with respect to probability measures due to P.L. Lions
[32], and It{\^o}'s formula along a flow of conditional measures, we derive the
dynamic programming Hamilton-Jacobi-Bellman equation, and prove the viscosity
property together with a uniqueness result for the value function. Finally, we
solve explicitly the linear-quadratic stochastic McKean-Vlasov control problem
and give an application to an interbank systemic risk model with common noise.

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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga