A Global Stochastic Maximum Principle for Forward-Backward Stochastic Control Systems with Quadratic Generators
Optimization and Control
2021-07-06 v2 Probability
Abstract
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.
Cite
@article{arxiv.2010.10680,
title = {A Global Stochastic Maximum Principle for Forward-Backward Stochastic Control Systems with Quadratic Generators},
author = {Mingshang Hu and Shaolin Ji and Rundong Xu},
journal= {arXiv preprint arXiv:2010.10680},
year = {2021}
}
Comments
31 pages