On the Existence of Optimal Policies in Stochastic Control

Abstract

In this paper a sufficient condition is presented for the existence of an optimal control for a system described by stochastic differential equations, the solutions of which are defined for any non-anticipative control policy, by the Girsanov measure transformation technique. The result is that if a Hamiltonian function achieves its infimum pointwise then an optimal nonanticipative policy exists.

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