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摘要翻译：
本文是一份初步研究报告的一部分，为一家风险咨询公司和学术研究提供参考。随机规划模型为不确定性环境下的决策提供了强有力的范例。在这些模型中，不确定性由一个离散的场景树来表示，得到的解的质量取决于生成的场景的质量。提出了一种新的基于混合高斯隐马尔可夫模型的场景生成技术。我们表明，我们的方法显式地捕捉到了随机过程的重要时变动力学（如自回归和跳跃）以及非高斯分布特征（如偏度和峰度）。我们的情景生成方法通过利用马尔可夫模型和高斯混合分布的可处理性，使情景生成具有更强的鲁棒性和情景分析能力。我们通过对FTSE-100数据进行数值实验，证明了我们的情景生成方法的好处。
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英文标题：
《Optimisation of Stochastic Programming by Hidden Markov Modelling based
Scenario Generation》
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作者：
Sovan Mitra
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最新提交年份：
2009
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分类信息：
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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一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are represented by a discrete scenario tree and the quality of the solutions obtained is governed by the quality of the scenarios generated. We propose a new technique to generate scenarios based on Gaussian Mixture Hidden Markov Modelling. We show that our approach explicitly captures important time varying dynamics of stochastic processes (such as autoregression and jumps) as well as non-Gaussian distribution characteristics (such as skewness and kurtosis). Our scenario generation method enables richer robustness and scenario analysis through exploiting the tractable properties of Markov models and Gaussian mixture distributions. We demonstrate the benefits of our scenario generation method by conducting numerical experiments on FTSE-100 data.
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PDF链接：
https://arxiv.org/pdf/0904.1131
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