西安交通大学 博士学位论文 多期风险度量与多阶段投资组合选择问题 学位申请人：刘嘉 指导教师：陈志平 学科名称：数学 2017年2月
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Multi-period Risk Measures and Multi-stage Portfolio Selection problems a dissertation submitted to Xi'an Jiaotong University in partial fulfillment of the requirement for the degree of Doctor of Natural so B Jia liu Supervisor: Prof. Zhiping Chen (Mathematics) February 2017
Multi-period Risk Measures and Multi-stage Portfolio Selection Problems A dissertation submitted to Xi’an Jiaotong University in partial fulfillment of the requirement for the degree of Doctor of Natural Science By Jia Liu Supervisor: Prof. Zhiping Chen (Mathematics) February 2017
摘要 论文题目:多期风险度量与多阶段投资组合选择问题 学科名称:数学 学位申请人:刘嘉 指导教师:陈志平教授 摘要 金融活动的本质是为了财富的快速增值,而金融活动的基本手段为投资运作.因 此,关于最优投资策略的研究一直都是金融学和运筹学的重点研究领域.随着静态投资 组合选择理论与方法的日趋完善,关于多期最优投资组合选择问题的研究近年来越来 越受到金融学者和运筹学工作者的关注.尤其在我国,受近几年证券市场不景气的影 响,以往带有投机色彩的短期交易行为很难再发挥作用,因此寻求稳健的多期投资策略 已是一个急迫的研究课题.然而,随着金融市场全球化的发展,现实的市场环境越来越 复杂,且时常会发生剧烈的变化,而投资者在选择投资策略时可能得不到完全的市场信 息.这些不确定因素促使我们考虑如何在复杂的市场环境下,构建能刻画市场环境动态 性的多期风险度量,由此构建能稳定获取收益且规避极端风险的多阶段投资组合选择 模型.综合运用统计方法与多种现代优化技术,本文将就这些问题展开如下的研究 1)作为构建复杂环境下新型多期风险度量的基础,我们首先总结多期风险度量应 该满足的基本性质,特别是多期风险度量特有的一个重要性质,时间相容性.同时,我 们综述并归纳已有文献中出现的多期风险度量的形式,并按其构造方式将多期风险度 量分为三类:终期财富风险度量,可加型风险度量,和递归型风险度量,进而给出这三 类多期风险度量的一般形式.对于每类风险度量,我们分别总结分析其数学性质,然后 讨论这三类多期风险度量之间的关系 (②)针对市场环境的时变特性,我们将机制转换模型,因子模型和时间序列模型相 结合,构建了一种新的联合信息框架.基于这个信息框架,我们提出了一个基于机制转 换的时间相容递归风险函数.当联合信息框架和基于机制转换的递归风险度量应用于 多期投资问题时,我们论述了如何有效转换和求解该多期投资问题.实证结果表明了联 合信息框架和相应多期投资模型的优异表现. (3)针对投资者不能精确获取市场完整信息的情况,我们使用分布式鲁棒优化技术 来处理一类随机损失的具体分布未知而只知道分布的矩信息的问题.我们提出了一种 基于可分期望条件函数的多期最坏情况风险度量.通过运用动态规划方法,我们导出了 相应多阶段鲁棒投资组合选择问题的解析最优解.实证结果表明这种多期最坏情况风 险度量和相应的多阶段鲁棒投资组合选择模型能规避市场最坏环境中的极端损失,做 出稳健的投资策略. 本研究得到国家自然科学基金(编号:70971109,71371152,11571270)资助
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ABSTRACT Title: Multi-period Risk Measures and Multi-stage Portfolio Selection Prob lems Descipline: Mathematics Applicant: Jia Liu Supervisor: Prof. Zhiping Chen ABSTRACT The essence of financial decision making problems is to pursuit higher profits, which is accomplished through choosing the optimal investment policy. Therefore, the optimal portfolio selection problem is always an important topic in financial optimization and operations research. Single-period portfolio selection problems have been extensively investigated, while the multi-period portfolio selection problem is attracting more and more attention in fields such as financial engineering and operations research. Espe. cially in China, the short-term investment can not earn stable profits any more due to the market depression. Hence, finding robust and optimal multi-stage portfolio becomes an urgent issue. Meanwhile, with the development of economic globalization, the market environment becomes more complicated, and the market state changes rapidly, it is thus very difficult for investors to obtain the complete market information. All these facts re- quire us to construct new multi-period risk measures which can capture the dynamics of market environment, and to construct resulting multi-stage portfolio selection models to gain stable returns while avoiding extreme risks. By simultaneously utilizing statistical methods and some modern optimization techniques, we will systematically investigate these issues from the following perspectives (1)As the basis for constructing new multi-period risk measures under complex market environment, we first review fundamental properties of multi-period risk measures, es pecially its time consistency. According to their structural properties, we divide current multi-period risk measures into three classes: terminal wealth risk measures, additive risk measures and recursive risk measures. Then we derive their generic forms. For each class, we survey typical formulations of multi-period risk measures in the literature, dis- cuss their mathematical properties and relationships (2)In order to describe the time-varying property of stochastic market, we propose a joint information framework by combining the regime switching model, the factor model The work is supported by the National Natural Science Foundation of China(Grant numbers: 70971109 71371152,11571270)
ABSTRACT Title: Multi-period Risk Measures and Multi-stage Portfolio Selection Problems Descipline: Mathematics Applicant: Jia Liu Supervisor: Prof. Zhiping Chen ABSTRACT The essence of financial decision making problems is to pursuit higher profits, which is accomplished through choosing the optimal investment policy. Therefore, the optimal portfolio selection problem is always an important topic in financial optimization and operations research. Single-period portfolio selection problems have been extensively investigated, while the multi-period portfolio selection problem is attracting more and more attention in fields such as financial engineering and operations research. Especially in China, the short-term investment can not earn stable profits any more due to the market depression. Hence, finding robust and optimal multi-stage portfolio becomes an urgent issue. Meanwhile, with the development of economic globalization, the market environment becomes more complicated, and the market state changes rapidly, it is thus very difficult for investors to obtain the complete market information. All these facts require us to construct new multi-period risk measures which can capture the dynamics of market environment, and to construct resulting multi-stage portfolio selection models to gain stable returns while avoiding extreme risks. By simultaneously utilizing statistical methods and some modern optimization techniques, we will systematically investigate these issues from the following perspectives* . (1) As the basis for constructing new multi-period risk measures under complex market environment, we first review fundamental properties of multi-period risk measures, especially its time consistency. According to their structural properties, we divide current multi-period risk measures into three classes: terminal wealth risk measures, additive risk measures and recursive risk measures. Then we derive their generic forms. For each class, we survey typical formulations of multi-period risk measures in the literature, discuss their mathematical properties and relationships. (2) In order to describe the time-varying property of stochastic market, we propose a joint information framework by combining the regime switching model, the factor model *The work is supported by the National Natural Science Foundation of China (Grant numbers: 70971109, 71371152, 11571270). III