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A Global Stochastic Maximum Principle for Forward-Backward Stochastic Control Systems with Quadratic Generators

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arxiv 2010.10680 v2 pith:KHZ6FXOW submitted 2020-10-21 math.OC math.PR

Mingshang Hu , Shaolin Ji , Rundong Xu This is my paper · ORCID
classification math.OCmath.PR
keywords stochasticcontrolbsdesforward-backwardgeneratorsglobalmaximumprinciple
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We study a stochastic optimal control problem for forward-backward control systems with quadratic generators. In order to establish the first and second-order variational and adjoint equations, we obtain a new estimate for one-dimensional linear BSDEs with unbounded stochastic Lipschitz coefficients involving bounded mean oscillation martingales (BMO-martingales for short) and prove the solvability for a class of multi-dimensional BSDEs with this type. Finally, a new global stochastic maximum principle is deduced.

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