Existence of an Optimal Control for Stochastic Systems with Nonlinear Cost Functional

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dc.creatorBuckdahn, Rainer
dc.creatorLabed, Boubakeur
dc.creatorRainer, Catherine
dc.creatorTamer, Lazhar
dc.date2009-02-16
dc.date.accessioned2026-07-07T12:42:16Z
dc.date.available2026-07-07T12:42:16Z
dc.descriptionWe consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate convexity assumptions on the coefficients of the forward and the backward equations we prove the existence of an optimal control on a suitable reference stochastic system. The proof is based on an approximation of the stochastic control problem by a sequence of control problems with smooth coefficients, admitting an optimal feedback control. The quadruplet formed by this optimal feedback control and the associated solution of the forward and the backward equations is shown to converge in law, at least along a subsequence. The convexity assumptions on the coefficients then allow to construct from this limit an admissible control process which, on an appropriate reference stochastic system, is optimal for our stochastic control problem.
dc.identifierhttps://arxiv.org/abs/0902.2693
dc.identifierhttp://arxiv.org/abs/0902.2693
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220020
dc.subjectProbability
dc.subject93E20, 93E03, 60H10, 34H05
dc.titleExistence of an Optimal Control for Stochastic Systems with Nonlinear Cost Functional
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