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。     

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．     

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.     

证券投资组合优化问题的强健性的锥优化方法(英文)

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.     

鲁棒信用风险优化的线性锥优化模型

考虑了具有强健性的信用风险优化问题. 根据最差条件在值风险度量信用风险的方法,建立了信用风险优化问题的模型. 由于信用风险的损失分布存在不确定性,考虑了两类不确定性区间,即箱子型区间和椭球型区间. 把具有强健性的信用风险优化问题分别转化成线性规划问题和二阶锥规划问题. 最后,通过一个信用风险问题的例子来说明此模型的有效性.     

Portfolio optimization by minimizing conditional value-at-risk via nondifferentiable optimization

Conditional Value-at-Risk (CVaR) is a portfolio evaluation function having appealing features such as sub-additivity and convexity. Although the CVaR function is nondifferentiable, scenario-based CVaR minimization problems can be reformulated as linear programs (LPs) that afford solutions via widely-used commercial softwares. However, finding solutions through LP formulations for problems having many financial instruments and a large number of price scenarios can be time-consuming as the dimension of the problem greatly increases. In this paper, we propose a two-phase approach that is suitable for solving CVaR minimization problems having a large number of price scenarios. In the first phase, conventional differentiable optimization techniques are used while circumventing nondifferentiable points, and in the second phase, we employ a theoretically convergent, variable target value nondifferentiable optimization technique. The resultant two-phase procedure guarantees infinite convergence to optimality. As an optional third phase, we additionally perform a switchover to a simplex solver starting with a crash basis obtained from the second phase when finite convergence to an exact optimum is desired. This three phase procedure substantially reduces the effort required in comparison with the direct use of a commercial stand-alone simplex solver (CPLEX 9.0). Moreover, the two-phase method provides highly-accurate near-optimal solutions with a significantly improved performance over the interior point barrier implementation of CPLEX 9.0 as well, especially when the number of scenarios is large. We also provide some benchmarking results on using an alternative popular proximal bundle nondifferentiable optimization technique.     

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.     

多目标条件风险值问题的等价定理

条件风险值问题是研究信用风险最优化的一种新的模型，本文研究了一类多目标条件风险值问题等价定理，我们引入了多个损失函数在对应的置信水平下关于一个证券组合的α-VaR损失值(最小信用风险值)和α-CVaR损失值(最小信用风险值对应的条件期望损失值或条件风险价值度量)概念，为了求得α-CVaR损失值下的弱：Pareto有效解，我们证明了它等价于求解另一个多目标规划问题的Pateto有效解，这样使得问题的求解变得简单．     

Measuring the coupled risks: A copula-based CVaR model

Integrated risk management for financial institutions requires an approach for aggregating risk types (such as market and credit) whose distributional shapes vary considerably. The financial institutions often ignore risks’ coupling influence so as to underestimate the financial risks. We constructed a copula-based Conditional Value-at-Risk (CVaR) model for market and credit risks. This technique allows us to incorporate realistic marginal distributions that capture essential empirical features of these risks, such as skewness and fat-tails while allowing for a rich dependence structure. Finally, the numerical simulation method is used to implement the model. Our results indicate that the coupled risks for the listed company’s stock maybe are undervalued if credit risk is ignored, especially for the listed company with bad credit quality.     

含MCVaR的投资组合优化统一模型

研究了Duarte提出的投资组合优化统一模型及条件风险价值(CVaR),分析了以CVaR为风险度量的投资组合优化模型的具体形式,建立了统一七种模型的投资组合优化统一模型,并发现统一模型是一个凸二次规划问题.