分数布朗运动驱动的SDDES平均场最优控制问题

Pub Date : 2017-06-20 DOI:10.37190/0208-4147.40.1.9
N. Agram, Soukaina Douissi, A. Hilbert
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引用次数: 1

摘要

研究一类具有赫斯特参数大于1 / 2的分数阶布朗运动时滞随机微分方程的平均场最优控制问题。分数阶布朗运动驱动的随机最优控制问题,由于分数阶布朗运动既不是马尔可夫过程,也不是半鞅,不能用经典方法进行研究。然而,利用分数阶白噪声演算结合测度函数微分的一些特殊工具,我们建立并证明了必要和充分的随机极大值原理。为了说明我们的研究,我们考虑了两个应用:我们解决了一个具有延迟的现金流的最优消费问题和一个具有延迟的线性二次(LQ)问题。
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Mean-field optimal control problem of SDDES driven by fractional Brownian Motion
We consider a mean-field optimal control problem for stochastic differential equations with delay driven by fractional Brownian motion with Hurst parameter greater than one half. Stochastic optimal control problems driven by fractional Brownian motion can not be studied using classical methods, because the fractional Brownian motion is neither a Markov process nor a semi-martingale. However, using the fractional White noise calculus combined with some special tools related to the differentiation for functions of measures, we establish and prove necessary and sufficient stochastic maximum principles. To illustrate our study, we consider two applications: we solve a problem of optimal consumption from a cash flow with delay and a linear-quadratique (LQ) problem with delay.
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