Modeling dependence based on mixture copulas and its application in risk management

This paper is concerned with the statistical modeling of the dependence structure of multivariate financial data using the copula, and the application of copula functions in VaR valuation. After the introduction of the pure copula method and the maximum and minimum mixture copula method, authors present a new algorithm based on the more generalized mixture copula functions and the dependence measure, and apply the method to the portfolio of Shanghai stock composite index and Shenzhen stock component index. Comparing with the results from various methods, one can find that the mixture copula method is better than the pure Gaussian copula method and the maximum and minimum mixture copula method on different VaR level.     

Deviation inequalities for an estimator of the conditional value-at-risk

In this paper, we present a deviation inequality for a common estimator of the conditional value-at-risk for bounded random variables. The result improves a deviation inequality which is obtained by Brown [D.B. Brown, Large deviations bounds for estimating conditional value-at-risk, Operations Research Letters 35 (2007) 722-730].     

An exact method for constrained maximization of the conditional value-at-risk of a class of stochastic submodular functions

We consider a class of risk-averse submodular maximization problems (RASM) where the objective is the conditional value-at-risk (CVaR) of a random nondecreasing submodular function at a given risk level. We propose valid inequalities and an exact general method for solving RASM under the assumption that we have an efficient oracle that computes the CVaR of the random function. We demonstrate the proposed method on a stochastic set covering problem that admits an efficient CVaR oracle for the random coverage function.     

Portfolio selection under distributional uncertainty: A relative robust CVaR approach

Robust optimization, one of the most popular topics in the field of optimization and control since the late 1990s, deals with an optimization problem involving uncertain parameters. In this paper, we consider the relative robust conditional value-at-risk portfolio selection problem where the underlying probability distribution of portfolio return is only known to belong to a certain set. Our approach not only takes into account the worst-case scenarios of the uncertain distribution, but also pays attention to the best possible decision with respect to each realization of the distribution. We also illustrate how to construct a robust portfolio with multiple experts (priors) by solving a sequence of linear programs or a second-order cone program.     

基于历史的情景模拟修正模型

文中基于情景模拟方法，提出了一种参考历史数据的修正模型。通过构成历史情景，在最大似然原则下确定情景集合的关键参数Θ。通过一个利率产品的数值实验，对原模型、修正模型与传统蒙特卡罗模型的在值风险估计值的精度进行比较，得到了理想的结果。     

基于CVaR理论的原油采购策略研究

在采购原油过程中,企业除了控制采购成本,还需控制潜在风险损失。文章利用金融领域的条件风险价值理论度量企业面临的潜在风险损失,结合随机规划理论构建了一个两阶段的原油采购决策模型,并结合我国原油进口实际进行了算例分析,分析结果对指导企业原油采购及风险控制具有参考意义。     

改进的粒子群算法及在CVaR模型中的应用

为了求解带有条件风险价值(CVaR)约束的均值-方差模型,提出一种基于广义学习和柯西变异的粒子群算法(CCPSO).在CCPSO算法中,为了提升种群跳出局部最优解的能力,引入一种广义学习策略,提升粒子向最优解飞行的概率;并引入一种动态变异概率,对粒子自身最优位置进行柯西变异,更好地引导种群的飞行;最后,根据全局最优粒子的运行状况,每间隔若干代对其进行变异,以产生全局新的领导者.在基准函数测试中,结果显示CCPSO算法有较好的运行结果.在CVaR模型投资组合优化中,与其它算法相比,CCPSO算法所获结果是有效的,并且优于其它算法.     

基于阿基米德Copula的投资组合风险分析

应用阿基米德Copula分析沪深股票市场投资组合风险,样本区间从2000年1月4日至2006年11月8日,共1639组有效数据．首先,由于金融数据不具有正态性,且是厚尾的,因而应用极值理论对边缘分布建模;然后,采用极大似然估计对给定的5个阿基米德Copula进行参数估计,从中选择能更好拟合实际数据相关性的Copula;最后,运用Monte Carlo模拟方法计算相应的风险价值（VaR）,确定最优的组合系数．结果表明,当组合系数β=0．33时,沪深股市投资组合风险最小．     

基于消费者选择偏好的可替代品订货策略

基于消费者选择偏好,建立了相应零售商利润-订单量的条件风险价值模型。以零售商利润为最优化目标,在市场总需求不确定时,考虑零售商风险偏好、消费者选择偏好及两种产品的可替代性,研究零售商的最优订货策略。研究结果表明,当产品订货量在一定范围时,产品替代性将失去作用:当两种产品总订货量在一定范围时,产品最优订货量随顾客偏好系数及产品替代系数的提高而增大,随替代产品顾客偏好系数和零售商风险规避程度的提高而减小:产品与替代产品间的顾客偏好系数差异越大,两产品总订货量越大。     

APARCH 模型在证券投资风险分析中的应用

本首先描述金融时间序列的一般特性，从收益率的波动性与分布两方面进行考虑，建立起计算时变风险值的VaR—APARCH模型，并应用VaR—APARCH模型在多种分布情形下测算了上证综合指数的风险，结果表明基于GED分布的VaR—APARCH模型能够较好地刻画高频时间序列的尖峰肥尾性及杠杆效应等特性。