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Stochastic control problems with delay

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We consider optimal control problems for systems described by stochastic differential equations with delay. We state conditions for certain classes of such systems under which the stochastic control problems become finite-dimensional. These conditions are illustrated with three applications. First, we solve some linear quadratic problems with delay. Then we find the optimal consumption rate in a financial market with delay. Finally, we solve explicitly a deterministic fluid problem with delay which arises from admission control in ATM communication networks.

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Correspondence to Harald Bauer.

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Bauer, H., Rieder, U. Stochastic control problems with delay. Math Meth Oper Res 62, 411–427 (2005).

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