基于CVaR风险测度的连续时间投资组合选择

发布时间：2018-06-25 06:07

本文选题：连续时间 + 均值-CVaR　；参考：《南京理工大学》2014年硕士论文

【摘要】：Markowitz均值-方差投资组合理论,开创了以数理方法研究金融问题的先河,取得了一系列影响深远的理论与实际应用的成果。数十年来,无数学者致力于均值-方差模型的理论拓展与应用研究,极大地丰富和发展了Markowitz组合选择理论。近年来,S. Emmer等研究了基于均值-CaR的连续时间组合选择问题,给出了该组合问题的有效前沿等有意义的结果。但该文只考量了资产价格过程服从几何布朗运动以及无风险意义下的损失界定。本文拟在S. Emmer等人工作的基础上,继续开展更为深入的探索,即研究基于均值-CVaR的连续时间组合选择问题。其中,资产价格过程服从跳一扩散过程以及基于无风险与风险资产组合意义下的损失界定。首先,分别就股价满足扩散模型和跳-扩散模型的情形,利用伊藤积分及创新性地构造了连续时间下CVaR的显示表达式；利用该表达式,构建了均值-CVaR模型,考虑到股价所服从的跳-扩散过程,运用matlab给出该模型数值解结构图以及最佳投资策略和相对应的有效前沿结构图。通过与均值-方差模型的对比,显示其合理性和优越性。其次,研究连续时间下财富效用-CVaR组合选择问题。以动态规划方法并辅以拉格朗日乘子法,得到了最优投资策略和有效前沿的解析解。
[Abstract]:Markowitz's mean-variance portfolio theory creates the first step in the study of financial problems by mathematical methods and has achieved a series of far-reaching theoretical and practical results. In recent decades, numerous scholars have devoted themselves to the theoretical development and application of mean-variance model, which has greatly enriched and developed Markowitz's combinatorial selection theory. In recent years, S. Emmer and others have studied the continuous time combinatorial selection problem based on mean value (-CaR), and obtained some useful results on the efficient frontier of the combinatorial problem. However, this paper only considers the definition of asset price process from geometric Brownian motion to risk-free loss. Based on the work of S. Emmer et al., this paper intends to further explore the problem of continuous time combination selection based on mean value (-CVaR). Among them, the asset price process service from jump-diffusion process and based on the risk-free and risk-free asset portfolio under the meaning of loss definition. Firstly, for the case that the stock price satisfies the diffusion model and the jump-diffusion model, the display expression of CVaR under continuous time is constructed by using Ito integral and innovatively, and the mean-CVaR model is constructed by this expression. Considering the jump-diffusion process of stock price, the numerical solution structure diagram of the model, the optimal investment strategy and the corresponding efficient frontier structure diagram are given by using matlab. The comparison with the mean-variance model shows its rationality and superiority. Secondly, the problem of wealth utility-CVaR portfolio selection in continuous time is studied. By using dynamic programming method and Lagrange multiplier method, the analytical solution of optimal investment strategy and efficient frontier is obtained.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.59;F224

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