基于MGARCH模型的情景树生成算法(英文)

Scenario Tree Generation Algorithms under MGARCH Models

多阶段随机最优化模型的质量依赖于描述不确定环境的情景树的质量.本文从以下几个方面对现有的情景树生成算法进行了改进:为恰当反映随机数据过程高阶矩的变化,我们提出了一个基于MGARCH模型的新模拟方法来生成情景;为改进现有情景生成的序列最优化方法,我们用MGARCH模型来递归估计随机数据过程的中心矩,设计了一个新的混合智能算法来求解序列最优化方法中所遇到的非凸规划问题,并由此导出了一个基于MGARCH模型的、可用于生成一般结构多阶段情景树的新型有效序列最优化方法.最后,利用中国和美国股票市场的金融交易数据,我们进行了一系列数值试验以说明我们算法的实用性、灵活性和有效性.

The quality of multi-stage stochastic optimization models depends heavily on the quality of the underlying scenario tree to describe the uncertain environment.Existing scenario generation algorithms are improved from the following aspects： to properly reflect variations in higher order moments of the underlying random data process,we propose a new simulation approach for scenario generation under the MGARCH model; to improve the current sequential optimization scenario generation method,the MGARCH model is used to recursively estimate central moments of the stochastic data process,and a new hybrid intelligent algorithm is designed to solve non-convex programming problems encountered during the sequential optimization process,derived from which is an efficient new-type sequential optimization method for general multistage scenario tree generation under MGARCH models;finally,numerical results with trade data from Chinese and American stock markets illustrate the practicality,flexibility and efficiency of our algorithms.