论文标题
带有二次发电机的前向后随机控制系统的全局随机最大原理
A Global Stochastic Maximum Principle for Forward-Backward Stochastic Control Systems with Quadratic Generators
论文作者
论文摘要
我们研究了带有二次发电机的前回控制系统的随机最佳控制问题。为了建立一阶变分和伴随方程，我们获得了具有无限的随机Lipschitz系数的一维线性BSDE的新估计值，该系数涉及有限的平均振荡Martingales（简短的BMO-MARTINGALES），并证明了与此类型类型的多类BSDESSDESSDESSDESSDESSDESSDESSDESSDESSDESSDESSDE。最后，推导了新的全球随机最大原理。
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.
