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We consider in this paper the efficient ways to generate multi-stage scenario trees. A general modified K-means clustering method is first presented to generate the scenario tree with a general structure. This method takes the time dependency of the simulated path into account. Based on the traditional and modified K-means analyses, the moment matching of multi-stage scenario trees is described as a linear programming (LP) problem. By simultaneously utilizing simulation, clustering, non-linear time series and moment matching skills, a sequential generation method and another new hybrid approach which can generate the whole multi-stage tree right off are proposed. The advantages of these new methods are: the vector autoregressive and multivariate generalized autoregressive conditional heteroscedasticity (VAR-MGARCH) model is adopted to properly reflect the inter-stage dependency and the time-varying volatilities of the data process, the LP-based moment matching technique ensures that the scenario tree generation problem can be solved more efficiently and the tree scale can be further controlled, and in the meanwhile, the statistical properties of the random data process are maintained properly. What is more important, our new LP methods can guarantee at least two branches are derived from each non-leaf node and thus overcome the drawback in relevant papers. We carry out a series of numerical experiments and apply the scenario tree generation methods to a portfolio management problem, which demonstrate the practicality, efficiency and advantages of our new approaches over other models or methods.  相似文献   
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赵华 《经济数学》2010,27(4):52-59
2005年以来人民币汇率均处于升值过程,而股市却经历了牛、熊市的历程.本文基于VECM-MGARCH模型实证研究了人民币汇率与我国股市处于牛、熊市期间二者之间的动态关系,结果发现,汇率和股价之间不存在线性的相互影响关系.就波动性而言,股市处于牛市期间,二者之间存在相互影响关系;熊市期间,这种非线性关系消失.人民币升值预期的减弱及股市的下跌是导致二者关系变化的主要原因.  相似文献   
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