Limit Theory for Controlled McKean-Vlasov Dynamics
Limit Theory for Controlled McKean-Vlasov Dynamics
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DOI：
10.1137/16m1095895
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发表时间：
2016-09
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影响因子：
--
通讯作者：
D. Lacker
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文献类型：
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作者：
D. Lacker
This paper rigorously connects the problem of optimal control of McKean-Vlasov dynamics with large systems of interacting controlled state processes. Precisely, the empirical distributions of near-optimal control-state pairs for the $n$-state systems, as $n$ tends to infinity, admit limit points in distribution (if the objective functions are suitably coercive), and every such limit is supported on the set of optimal control-state pairs for the McKean-Vlasov problem. Conversely, any distribution on the set of optimal control-state pairs for the McKean-Vlasov problem can be realized as a limit in this manner. Arguments are based on controlled martingale problems, which lend themselves naturally to existence proofs; along the way it is shown that a large class of McKean-Vlasov control problems admit optimal Markovian controls.
