A Probabilistic Numerical Method for Optimal Multiple Switching Problems in High Dimension
A Probabilistic Numerical Method for Optimal Multiple Switching Problems in High Dimension
复制标题
高维最优多重切换问题的概率数值方法
DOI：
10.1137/120897298
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
H. Pham
中科院分区：
文献类型：
--
作者：
R. Aïd;L. Campi;N. Langrené;H. Pham
在本文中，我们提出了一种结合动态规划、蒙特卡罗模拟和局部基回归的概率数值算法来解决无限范围内的非平稳最优多重切换问题。我们根据用于离散问题的时间步长、用于近似条件期望的回归基础以及截断时间范围来提供该方法的收敛速度。为了使该方法适用于高维和长时间范围的问题，我们将内存缩减方法扩展到一般欧拉方案，以便在执行数值解析时不需要存储蒙特卡罗模拟路径。然后，我们将该算法应用于第八维电厂最优投资模型，即采用两种不同的技术和六个随机因素。
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the regression basis used to approximate conditional expectations, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants in dimension eight, i.e. with two different technologies and six random factors.