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摘要翻译：
本文提出了一种结合动态规划、Monte Carlo模拟和局部基回归的概率数值算法来求解无限时域内的非平稳最优多重切换问题。我们根据离散问题所用的时间步长、回归中涉及的局部超立方体的大小和截断时间范围给出了该方法的收敛速度。为了使该方法适用于高维、长时间的问题，我们将一种内存缩减方法推广到一般的欧拉格式，这样在进行数值求解时，就不需要存储蒙特卡罗模拟路径。然后，我们将该算法应用于一个电厂最优投资模型。该模型考虑了电力需求、联合燃料价格、碳价格和电厂随机停电等因素。它计算了每一代技术的最佳投资水平，作为一个整体考虑，W.R.T。电力现货价格。这个电价本身是根据一个新的扩展结构模型建立的。特别是，它是几个因素的函数，其中装机容量。在一个实际的八维数值问题上，即在两种不同技术和六个随机因素下，说明了最优发电组合的演化。
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英文标题：
《A probabilistic numerical method for optimal multiple switching problem
and application to investments in electricity generation》
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作者：
Ren\'e A\"id (FiME Lab), Luciano Campi (CREST, LAGA), Nicolas
Langren\'e (LPMA), Huy\^en Pham (CREST, LPMA)
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最新提交年份：
2012
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分类信息：
一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
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 size of the local hypercubes involved in the regressions, 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. This model takes into account electricity demand, cointegrated fuel prices, carbon price and random outages of power plants. It computes the optimal level of investment in each generation technology, considered as a whole, w.r.t. the electricity spot price. This electricity price is itself built according to a new extended structural model. In particular, it is a function of several factors, among which the installed capacities. The evolution of the optimal generation mix is illustrated on a realistic numerical problem in dimension eight, i.e. with two different technologies and six random factors.
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PDF链接：
https://arxiv.org/pdf/1210.8175
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