基于历史数据集生成情景树的两种新方法∗

摘要

A scenario tree is an efficient way to represent the stochastic parameters in decision problems under uncertainty. Two new historical data based scenario tree generation methods are proposed in this paper. Considering the financial management background, an LP model used to detect arbitrage opportunity is developed. It is easy to exclude the arbitrage oppor-tunity when using two new methods to generate the scenario tree, the generated scenario tree includes the past realistic evolution of the historical data, and the distribution determined by the scenario tree can properly fit the empirical distribution of asset returns;moreover, the gen-erated scenario tree could describe the trend of the returns of the assets, providing two efficient scenario analysis tools for dynamic portfolio selection problems.%　　情景树是描述不确定性决策问题中随机参数的一种有效方式。本文提出了两种基于历史数据集生成情景树的新方法。结合金融背景，给出了如何检测套利机会的线性规划模型。两种新方法在生成情景时能够容易地规避套利机会，并且所生成的情景包含了部分历史数据真实的演化模式，能够比较好地拟合资产收益的经验分布函数；此外，所得情景可以恰当地描述资产收益未来的走势，为动态投资组合选择问题提供了两种有效的情景分析工具。