多元VaR的特征及其应用研究

发布时间：2018-05-17 05:08

本文选题：多元VaR + 极值理论　；参考：《南京理工大学》2017年硕士论文

【摘要】：在经济、保险和金融领域,风险价值(VaR)是广泛使用的针对一个特定金融资产投资组合损失风险的度量工具。对于一个给定的投资组合,持有期间以及概率α,100α%VaR被定义为一个临界阈值,使得投资组合在持有期内损失超过这个阈值的概率为α。也就是说,VaR是损失分布的分位数,有很好的分析性质,而且便于理解。本文基于Raúl Torres et.al(2015)关于多元VaR的研究,提出了基于高维中位数的多元VaR,即MVaR_α~u(X),探讨了MVaR_α~u(X)的性质、研究了MVaR_α~u(X)-均值最优投资组合问题,分析了MVaR_α~u(X)的鲁棒性。首先本文给出了基于高维中位数的多元VaR,即MVaR_α~u(X)的定义,研究了MVaR_α~u(X)的良好的分析性质,基于MVaR_α~u(X)是由多变量分位数和高维中位数所确定,利用极值理论给出了多变量分位数的样本外估计,同时给出了高维中位数的算法,从而解决了MVaR_α~u(X)的计算问题。其次,针对MVaR_α~u(X),类似一元VaR-均值的情形,提出了MVaR_α~u(X)-均值的最优投资组合问题,采用遗传算法对MVaR_α~u(X)-均值模型进行实证分析。该研究从理论上推广了经典的VaR-均值组合优化问题,结论显示该研究具有很好的经济学意义。最后,将Raúl Torres et.al(2015)提出的基于均值的多元VaR,即VaR_α~u(X)作为参照,对MVaR_α~u(X)进行鲁棒性的分析,从离群值和风险水平影响两个角度将MVaR_α~u(X)和VaR_α~u(X)比较,说明MVaR_α~u(X)的鲁棒性相较于VaR_α~u(X)更好。
[Abstract]:In the fields of economy, insurance and finance, Value-at-risk (VaR) is a widely used tool for measuring the loss risk of a particular financial asset portfolio. For a given portfolio, the holding period and probability 伪 -100 伪 VaR are defined as a critical threshold, so that the probability of portfolio loss exceeding this threshold during the holding period is 伪. That is to say, VaR is the quantile of loss distribution, which has good analytical properties and is easy to understand. In this paper, based on Ra 煤 l Torres et. Alan2015), we put forward multivariate VaR based on high dimensional median, discuss the properties of MVaR _ 伪, study the optimal portfolio problem of MVaR _ 伪, and analyze the robustness of MVaR _ 伪 UX). Firstly, this paper gives the definition of multivariate VaR based on high dimensional median, that is, MVaR _ 伪, and studies the good analytical properties of MVaR _ 伪. Based on the fact that MVaR _ 伪 is determined by multivariate quantiles and high dimensional median, By using the extreme value theory, the estimation of multivariate quantiles is given, and the algorithm of high dimensional median is given, thus solving the problem of calculating MVaR伪. Secondly, in the case of MVaR _ 伪, similar to one-variable VaR-means, the optimal portfolio problem of MVaR _ 伪 is put forward, and the genetic algorithm is used to analyze the model of MVaR _ 伪. This paper generalizes the classical VaR-Means combinatorial optimization problem theoretically, and the conclusion shows that the research has good economic significance. Finally, this paper analyzes the robustness of multiple VaRs based on the mean value (VaR伪) proposed by Ra 煤 l Torres et. Alan2015, and analyses the robustness of MVaR伪. From the outlier value and the risk level influence, we compare the robustness of MVaR伪 and VaR伪. The results show that the robustness of MVaR _ 伪 is better than that of RV _ 伪.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.59

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