This paper solves a mean-field type hierarchical optimal control problem in electricity market. The authors consider n − 1 prosumers and one producer. The ith prosumer, for 1 < i < n, is a leader of the (i − 1)th prosumer and is a follower of the (i + 1)th prosumer. The first player (agent) is the follower at the bottom whereas the nth is the leader at the top. The problem is described by a linear jump-diffusion system of conditional mean-field type, where the conditioning is with respect to common noise, and a quadratic cost functional involving, the square of the conditional expectation of the controls of the agents. The authors provide a semi-explicit solution of the corresponding mean-field-type hierarchical control problem with common noise. Finally, the authors illustrate the obtained result via a numerical example with two different scenarios.

本文解决了电力市场中的一个平均场型分层最优控制问题。作者考虑了n -1 个生产者和一个生产者。第i个产消者，对于 1 < i < n，是第 ( i − 1) 个产消者的领导者，并且是第 ( i + 1) 个产消者的追随者。第一个玩家（代理）是底部的跟随者，而n这是顶部的领导者。该问题由条件平均场类型的线性跳跃扩散系统描述，其中条件是相对于公共噪声，以及涉及代理控制的条件期望的平方的二次成本函数。作者提供了具有公共噪声的相应平均场型分层控制问题的半显式解决方案。最后，作者通过具有两种不同场景的数值示例说明了所获得的结果。