论文标题
带有二次发电机和样本约束的前向后随机控制系统的随机最大原理
A Stochastic Maximum Principle for Forward-backward Stochastic Control Systems with Quadratic Generators and Sample-wise Constraints
论文作者
论文摘要
本文研究了前向后的随机控制系统的随机最大原理（SMP），其中向后状态方程的特征是向后随机微分方程（BSDE）具有二次生长，而在终端时间的正向状态则以cONVEX设置为基础，并限制为概率。借助BSDE的理论，具有二次生长和有限的平均振荡（BMO）Martingales，我们采用终端扰动方法和Ekeland的变分原理来获得动态的随机原理。主要结果在数学金融中具有广泛的应用，我们研究了一个强大的递归效用最大化问题，禁止破产。
This paper examines the stochastic maximum principle (SMP) for a forward-backward stochastic control system where the backward state equation is characterized by the backward stochastic differential equation (BSDE) with quadratic growth and the forward state at the terminal time is constrained in a convex set with probability one. With the help of the theory of BSDEs with quadratic growth and the bounded mean oscillation (BMO) martingales, we employ the terminal perturbation approach and Ekeland's variational principle to obtain a dynamic stochastic maximum principle. The main result has a wide range of applications in mathematical finance and we investigate a robust recursive utility maximization problem with bankruptcy prohibition as an example.
