Regress-Later Monte Carlo for Optimal Inventory Control with applications in energy
Regress-Later Monte Carlo for Optimal Inventory Control with applications in energy
复制标题
用于能源应用的最优库存控制的稍后回归蒙特卡罗
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Jan Palczewski
中科院分区：
文献类型：
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作者：
Alessandro Balata;Jan Palczewski
提出了一种基于蒙特-卡罗的离散时间随机最优控制问题的数值解法。这些都是最优控制问题，其中控制只影响一个确定性不断发展的库存过程在一个紧凑的状态空间，而随机的基本过程表现出来，通过目标功能。我们提出了一个回归后修改传统的回归蒙特卡洛，它允许解耦库存水平在两个连续的时间步长，并包括在回归的基础函数的依赖库存水平。我们开发了一个向后建设的库存轨迹，使我们能够使用的Longstaff-Schwartz型避免嵌套模拟的政策迭代。我们的算法改进了文献和实践中大量使用的网格离散化程序，以及最近提出的控制随机化[Kharroubi等人（2014）Monte Carlo Methods and Applications，20（2），pp. 145-165]。我们验证了我们的方法上的两个数值例子：一个是用于比较不同的方法在文献中的能源套利的基准问题，另一个是一个高维问题的管理电池的目的是协助操作的风力涡轮机在提供电力的一组建筑物的成本效益的方式。
We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory process on a compact state space while the random underlying process manifests itself through the objective functional. We propose a Regress Later modification of the traditional Regression Monte Carlo which allows to decouple inventory levels in two successive time steps and to include in the basis functions of the regression the dependence on the inventory levels. We develop a backward construction of trajectories for the inventory which enables us to use policy iteration of Longstaff-Schwartz type avoiding nested simulations. Our algorithm improves on the grid discretisation procedure largely used in literature and practice, and on the recently proposed control randomisation by [Kharroubi et al. (2014) Monte Carlo Methods and Applications, 20(2), pp. 145-165]. We validate our approach on two numerical examples: one is a benchmark problem of energy arbitrage used to compare different methods available in literature, the other is a high-dimensional problem of the management of a battery with the purpose of assisting the operations of a wind turbine in providing electricity to a group of buildings in a cost effective way.