基于多目标CVaR模型的证券组合投资的风险度量和策略

本文首先定义了多损失函数下的-αVaR,-αCVaR损失值以及-αCVaR损失值的等价函数,给出了多目标CVaR模型.然后,基于多目标CVaR模型,建立了一个多目标证券组合投资优化模型,得出在多置信水平下的证券组合投资比例和CVaR值,据此建立一种证券组合投资的降低风险优化模型.其降低风险策略是在收益率不变的情形下降低风险和总投资比例.数值实验表明,这种策略是可以通过明显地减少总投资比例来达到降低风险的目的.     

基于CVaR的债券投资组合模型

针对债券投资组合中的风险度量难题,用CVaR作为风险度量方法,构建了基于CVaR的债券投资组合优化模型.采用历史模拟算法处理模型中的随机收益率向量,将随机优化模型转化为确定性优化模型,并且证明了算法的收敛性.通过线性化技术处理CVaR中的非光滑函数,将该模型转化为一般的线性规划模型.结合10只债券的组合投资实例,验证了模型与算法的有效性.     

基于相对鲁棒CVaR的电网投资项目组合优化模型研究

在新一轮电改的背景下,电网投资将面临更多的不确定性风险,亟需落实精准投资以降低投资风险.将相对鲁棒CVaR风险度量模型应用于电网投资项目组合优化中,构建了基于相对鲁棒CVaR的电网投资项目组合优化模型,并通过蒙特卡洛仿真和K-means聚类方法进行随机样本的生成与削减.算例结果表明,相对鲁棒CVaR模型具有极好的鲁棒性,能够在相对最坏情景下保证电网投资风险的最小化;同时,相对于绝对鲁棒CVaR模型减小了决策结果的保守性.     

基于Pair-Copula-GARCH模型与CVaR的时变投资组合优化

以过去的信息为条件,以一致性风险度量CVaR为优化目标,以组合收益率为约束条件,建立了时变投资组合优化模型,通过基于pair-copula-GARCH模型的蒙特卡洛模拟方法得到未来某时刻收益率的多个可能情景,并引入一个特殊函数实现了投资组合模型的线性化,得到了最优投资组合策略.最后针对提出的模型进行了实例分析.     

求解带有交易费的CVaR投资组合模型的L-S算法

本文假设投资者是风险厌恶型,用CVaR作为测量投资组合风险的方法.在预算约束的条件下,以最小化CVaR为目标函数,建立了带有交易费用的投资组合模型.将模型转化为两阶段补偿随机优化模型,构造了求解模型的随机L-S算法.为了验证算法的有效性,用中国证券市场中的股票进行数值试验,得到了最优投资组合、VaR和CVaR的值.而且对比分析了有交易费和没有交易费的最优投资组合的不同,给出了相应的有效前沿.     

基于CVaR的最优投资组合模型算法分析

通过引入光滑因子,改进了基于条件风险值(CVaR)的最优投资组合线性模型,并详细介绍了以VaR最小为目标函数的最优投资组合模型的算法设计思想与过程.     

基于CVaR投资组合优化问题的光滑化方法

对选定的风险资产进行组合投资,以条件风险价值(CVaR)作为度量风险的工具,建立单期投资组合优化问题的CVaR模型。目标函数中含有多重积分与plus函数,产生情景矩阵将多重积分计算转化成求和运算,提出plus函数的一个新的一致光滑逼近函数并给出求解CVaR模型的光滑化方法,最后的实证研究表明了本文算法的优越性。     

CVaR鲁棒均值-CVaR投资组合模型与求解

传统的均值-风险(包括方差、VaR、CVaR等)组合选择模型在计算最优投资组合时,常假定均值是已知的常值,但在实际资产配置中,收益的均值估计会有偏差,即存在着估计风险.在利用CVaR测度估计风险的基础上,研究了CVaR鲁棒均值-CVaR投资组合选择模型,给出了另外两种不同的求解方法,即对偶法和光滑优化方法,并探讨了它们的相关性质及特征,数值实验表明在求解大样本或者大规模投资组合选择问题上,对偶法和光滑优化方法在计算上是可行且有效的.     

CVaR风险度量模型在投资组合中的运用

风险价值(VaR)是近年来金融机构广泛运用的风险度量指标，条件风险价值(CVaR)是VaR的修正模型，也称为平均超额损失或尾部VaR，它比VaR具有更好的性质。在本中，我们将运用风险度量指标VaR和CVaR，提出一个新的最优投资组合模型。介绍了模型的算法，而且利用我国的股票市场进行了实证分析，验证了新模型的有效性，为制定合理的投资组合提供了一种新思路。     

基于CVaR的多目标投资组合模型

金融市场的发展与完善,以及人民收入水平的提高,使越来越多人关注金融投资并成为热点.理性的投资者总是期望风险尽可能低同时收益又尽可能高,而且希望投资的资产易于管理和管理成本低.考虑投资者多个目标的要求,将运用CVaR风险度量方法,提出一个均值—CVaR—资产数目的多目标投资组合模型,并利用多目标粒子群算法对模型进行实证分析,验证新模型的可行性和有效性,为热衷投资的投资者进行投资组合提供一个新方法.     

信用资产组合优化的"条件在险值-补偿"型随机规划模型

本文对于信用资产组合的优化问题给出了一个稳健的模型，所建模型涉及了条件在险值（CVaR）风险度量以及具有补偿限制的随机线性规划框架，其思想是在CVaR与信用资产组合的重构费用之间进行权衡，并降低解对于随机参数的实现的敏感性．为求解相应的非线性规划，本文将基本模型转化为一系列的线性规划的求解问题．     

Conditional value-at-risk in portfolio optimization: Coherent but fragile

We evaluate conditional value-at-risk (CVaR) as a risk measure in data-driven portfolio optimization. We show that portfolios obtained by solving mean-CVaR and global minimum CVaR problems are unreliable due to estimation errors of CVaR and/or the mean, which are magnified by optimization. This problem is exacerbated when the tail of the return distribution is made heavier. We conclude that CVaR, a coherent risk measure, is fragile in portfolio optimization due to estimation errors.     

Robust portfolio optimization with copulas

Conditional Value at Risk (CVaR) is widely used in portfolio optimization as a measure of risk. CVaR is clearly dependent on the underlying probability distribution of the portfolio. We show how copulas can be introduced to any problem that involves distributions and how they can provide solutions for the modeling of the portfolio. We use this to provide the copula formulation of the CVaR of a portfolio. Given the critical dependence of CVaR on the underlying distribution, we use a robust framework to extend our approach to Worst Case CVaR (WCVaR). WCVaR is achieved through the use of rival copulas. These rival copulas have the advantage of exploiting a variety of dependence structures, symmetric and not. We compare our model against two other models, Gaussian CVaR and Worst Case Markowitz. Our empirical analysis shows that WCVaR can asses the risk more adequately than the two competitive models during periods of crisis.     

An exact solution to a robust portfolio choice problem with multiple risk measures under ambiguous distribution

This paper proposes a unified framework to solve distributionally robust mean-risk optimization problem that simultaneously uses variance, value-at-risk (VaR) and conditional value-at-risk (CVaR) as a triple-risk measure. It provides investors with more flexibility to find portfolios in the sense that it allows investors to optimize a return-risk profile in the presence of estimation error. We derive a closed-form expression for the optimal portfolio strategy to the robust mean-multiple risk portfolio selection model under distribution and mean return ambiguity (RMP). Specially, the robust mean-variance, robust maximum return, robust minimum VaR and robust minimum CVaR efficient portfolios are all special instances of RMP portfolios. We analytically and numerically show that the resulting portfolio weight converges to the minimum variance portfolio when the level of ambiguity aversion is in a high value. Using numerical experiment with simulated data, we demonstrate that our robust portfolios under ambiguity are more stable over time than the non-robust portfolios.     

Credit risk optimization with Conditional Value-at-Risk criterion

This paper examines a new approach for credit risk optimization. The model is based on the Conditional Value-at-Risk (CVaR) risk measure, the expected loss exceeding Value-at-Risk. CVaR is also known as Mean Excess, Mean Shortfall, or Tail VaR. This model can simultaneously adjust all positions in a portfolio of financial instruments in order to minimize CVaR subject to trading and return constraints. The credit risk distribution is generated by Monte Carlo simulations and the optimization problem is solved effectively by linear programming. The algorithm is very efficient; it can handle hundreds of instruments and thousands of scenarios in reasonable computer time. The approach is demonstrated with a portfolio of emerging market bonds. Received: November 1, 1999 / Accepted: October 1, 2000?Published online December 15, 2000     

A closed-form solution of the Black–Litterman model with conditional value at risk

We consider a portfolio optimization problem of the Black–Litterman type, in which we use the conditional value-at-risk (CVaR) as the risk measure and we use the multi-variate elliptical distributions, instead of the multi-variate normal distribution, to model the financial asset returns. We propose an approximation algorithm and establish the convergence results. Based on the approximation algorithm, we derive a closed-form solution of the portfolio optimization problems of the Black–Litterman type with CVaR.     

证券投资组合优化问题的强健性的锥优化方法(英)

本文研究了具有强健性的证券投资组合优化问题.模型以最差条件在值风险为风险度量方法,并且考虑了交易费用对收益的影响.当投资组合的收益率概率分布不能准确确定但是在有界的区间内,尤其是在箱型区间结构和椭球区域结构内时,我们可以把具有强健性的证券投资组合优化问题的模型分别转化成线性规划和二阶锥规划形式.最后,我们用一个真实市场数据的算例来验证此方法.     

A smoothing method for solving portfolio optimization with CVaR and applications in allocation of generation asset

This paper focuses on the computation issue of portfolio optimization with scenario-based CVaR. According to the semismoothness of the studied models, a smoothing technology is considered, and a smoothing SQP algorithm then is presented. The global convergence of the algorithm is established. Numerical examples arising from the allocation of generation assets in power markets are done. The computation efficiency between the proposed method and the linear programming (LP) method is compared. Numerical results show that the performance of the new approach is very good. The remarkable characteristic of the new method is threefold. First, the dimension of smoothing models for portfolio optimization with scenario-based CVaR is low and is independent of the number of samples. Second, the smoothing models retain the convexity of original portfolio optimization problems. Third, the complicated smoothing model that maximizes the profit under the CVaR constraint can be reduced to an ordinary optimization model equivalently. All of these show the advantage of the new method to improve the computation efficiency for solving portfolio optimization problems with CVaR measure.