本文選題：多元VaR + 極值理論�。� 參考：《南京理工大學》2017年碩士論文

【摘要】：在經濟、保險和金融領域,風險價值(VaR)是廣泛使用的針對一個特定金融資產投資組合損失風險的度量工具。對于一個給定的投資組合,持有期間以及概率α,100α%VaR被定義為一個臨界閾值,使得投資組合在持有期內損失超過這個閾值的概率為α。也就是說,VaR是損失分布的分位數(shù),有很好的分析性質,而且便于理解。本文基于Raúl Torres et.al(2015)關于多元VaR的研究,提出了基于高維中位數(shù)的多元VaR,即MVaR_α~u(X),探討了MVaR_α~u(X)的性質、研究了MVaR_α~u(X)-均值最優(yōu)投資組合問題,分析了MVaR_α~u(X)的魯棒性。首先本文給出了基于高維中位數(shù)的多元VaR,即MVaR_α~u(X)的定義,研究了MVaR_α~u(X)的良好的分析性質,基于MVaR_α~u(X)是由多變量分位數(shù)和高維中位數(shù)所確定,利用極值理論給出了多變量分位數(shù)的樣本外估計,同時給出了高維中位數(shù)的算法,從而解決了MVaR_α~u(X)的計算問題。其次,針對MVaR_α~u(X),類似一元VaR-均值的情形,提出了MVaR_α~u(X)-均值的最優(yōu)投資組合問題,采用遺傳算法對MVaR_α~u(X)-均值模型進行實證分析。該研究從理論上推廣了經典的VaR-均值組合優(yōu)化問題,結論顯示該研究具有很好的經濟學意義。最后,將Raúl Torres et.al(2015)提出的基于均值的多元VaR,即VaR_α~u(X)作為參照,對MVaR_α~u(X)進行魯棒性的分析,從離群值和風險水平影響兩個角度將MVaR_α~u(X)和VaR_α~u(X)比較,說明MVaR_α~u(X)的魯棒性相較于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 偽 -100 偽 VaR are defined as a critical threshold, so that the probability of portfolio loss exceeding this threshold during the holding period is 偽. 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 _ 偽, study the optimal portfolio problem of MVaR _ 偽, and analyze the robustness of MVaR _ 偽 UX). Firstly, this paper gives the definition of multivariate VaR based on high dimensional median, that is, MVaR _ 偽, and studies the good analytical properties of MVaR _ 偽. Based on the fact that MVaR _ 偽 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偽. Secondly, in the case of MVaR _ 偽, similar to one-variable VaR-means, the optimal portfolio problem of MVaR _ 偽 is put forward, and the genetic algorithm is used to analyze the model of MVaR _ 偽. 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偽) proposed by Ra 煤 l Torres et. Alan2015, and analyses the robustness of MVaR偽. From the outlier value and the risk level influence, we compare the robustness of MVaR偽 and VaR偽. The results show that the robustness of MVaR _ 偽 is better than that of RV _ 偽.
【學位授予單位】：南京理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F224;F830.59

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