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arXiv · 1708.03004

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

Qingxin Meng·Qiuhong Shi·Maoning Tang
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Abstract

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 $\varepsilon $-near optimal control in a local form with an error order of exact $\varepsilon ^{% \frac{1}{2}}.$ Moreover, under additional convexity conditions on Hamiltonian function, we prove that an $\varepsilon $-maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality.

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Qingxin Meng, Qiuhong Shi, Maoning Tang. 2017-08-09. Partial Information Near-Optimal Control of Forward-Backward Stochastic Differential System with Observation Noise. https://arxiv.org/abs/1708.03004

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