Partial Information Near-Optimal Control of Forward-Backward Stochastic Differential System with Observation Noise

This paper first makes an attempt to investigate the partial information near optimal control of systems governed by forward-backward stochastic differential equations with observation noise under the assumption of a convex control domain. By Ekeland's variational principle and some basic estimates for state processes and adjoint processes, we establish the necessary conditions for any ε -near optimal control in a local form with an error order of exact ε
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. Moreover, under additional convexity conditions on Hamiltonian function, we prove that an ε - maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality.