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IMA Journal of Mathematical Control and Information 1987 4(4):301-320; doi:10.1093/imamci/4.4.301
© 1987 by Institute of Mathematics and its Applications
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Existence Theory for a Stochastic Bolza Problem

PHILIP D. LOEWEN

Department of Mathematics, University of British Columbia Vancouver V6T 1Y4, Canada

The direct method is used to prove the existence of optimal open-loop controls for stochastic optimal control problems in Bolza form. Instead of requiring the control set to be compact, as previous authors have done, we impose a superquadratic growth condition on the running cost. Degeneracy of the diffusion coefficient is allowed by this approach—in fact, the main result reduces to a well known deterministic theorem when the diffusion coefficient is zero.


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