论文标题
随机时间变化的Volterra游戏的最大原则
Maximum principles for stochastic time-changed Volterra games
论文作者
论文摘要
我们研究了两个玩家之间的随机差异游戏，控制着前向随机的Volterra积分方程（FSVIE）。每个玩家都必须优化自己的性能功能，其中包括向后的随机微分方程（BSDE）。所考虑的动态是由随时间变化的莱维噪声驱动的，并具有绝对连续的时间变化过程。我们证明了足够的最大原则来表征NASH平衡和相关的最佳策略。为此，我们在部分信息和非期望的随机导数下使用控制技术。零和游戏是特定情况。
We study a stochastic differential game between two players, controlling a forward stochastic Volterra integral equation (FSVIE). Each player has to optimize his own performance functional which includes a backward stochastic differential equation (BSDE). The dynamics considered are driven by time-changed Lévy noises, with absolutely continuous time-change process. We prove a sufficient maximum principle to characterize Nash equilibria and the related optimal strategies. For this we use techniques of control under partial information, and the non-anticipating stochastic derivative. The zero-sum game is presented as a particular case.
