论文标题
离散时间平均场随机最佳控制问题的最大原理
Maximum principle for discrete time mean-field stochastic optimal control problems
论文作者
论文摘要
在本文中，我们研究了平均场类型的离散时间随机微分方程（SDE）的最佳控制，其中系数可以依赖于法律的函数和过程状态。我们为离散时间随机最佳控制问题建立了最大原理的新版本。此外，成本功能也是平均场类型的。这种最大原理与经典原理不同，因为我们将新的离散时间向后（矩阵）随机方程式引入。基于离散的向后随机方程，其中伴随方程式视为具有平均场的离散后SDE，我们为随机离散的最佳控制问题获得了必要的一阶和足够的最佳条件。为了验证，我们将结果应用于生产和消费选择优化问题。
In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new version of the maximum principle for discrete-time stochastic optimal control problems. Moreover, the cost functional is also of the mean-field type. This maximum principle differs from the classical principle since we introduce new discrete-time backward (matrix) stochastic equations. Based on the discrete-time backward stochastic equations where the adjoint equations turn out to be discrete backward SDEs with mean field, we obtain necessary first-order and sufficient optimality conditions for the stochastic discrete optimal control problem. To verify, we apply the result to production and consumption choice optimization problem.
