共查询到20条相似文献,搜索用时 28 毫秒
1.
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. 相似文献
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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。 相似文献
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Włodzimierz Ogryczak Tomasz Śliwiński 《Computational Optimization and Applications》2011,50(3):591-595
This note is focused on computational efficiency of the portfolio selection models based on the Conditional Value at Risk
(CVaR) risk measure. The CVaR measure represents the mean shortfall at a specified confidence level and its optimization may
be expressed with a Linear Programming (LP) model. The corresponding portfolio selection models can be solved with general
purpose LP solvers. However, in the case of more advanced simulation models employed for scenario generation one may get several
thousands of scenarios. This may lead to the LP model with huge number of variables and constraints thus decreasing the computational
efficiency of the model. To overcome this difficulty some alternative solution approaches are explored employing cutting planes
or nondifferential optimization techniques among others. Without questioning importance and quality of the introduced methods
we demonstrate much better performances of the simplex method when applied to appropriately rebuilt CVaR models taking advantages
of the LP duality. 相似文献
4.
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. 相似文献
5.
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. 相似文献
6.
Index tracking problems are concerned in this paper. A CVaR risk constraint is introduced into general index tracking model to control the downside risk of tracking portfolios that consist of a subset of component stocks in given index. Resulting problem is a mixed 0?C1 and non-differentiable linear programming problem, and can be converted into a mixed 0?C1 linear program so that some existing optimization software such as CPLEX can be used to solve the problem. It is shown that adding the CVaR constraint will have no impact on the optimal tracking portfolio when the index has good (return increasing) performance, but can limit the downside risk of the optimal tracking portfolio when index has bad (return decreasing) performance. Numerical tests on Hang Seng index tracking and FTSE 100 index tracking show that the proposed index tracking model is effective in controlling the downside risk of the optimal tracking portfolio. 相似文献
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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. 相似文献
10.
This paper is concerned with solving single CVaR and mixed CVaR minimization problems. A CHKS-type smoothing sample average
approximation (SAA) method is proposed for solving these two problems, which retains the convexity and smoothness of the original
problem and is easy to implement. For any fixed smoothing constant ε, this method produces a sequence whose cluster points are weak stationary points of the CVaR optimization problems with probability
one. This framework of combining smoothing technique and SAA scheme can be extended to other smoothing functions as well.
Practical numerical examples arising from logistics management are presented to show the usefulness of this method. 相似文献
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CVaR风险度量模型在投资组合中的运用 总被引:9,自引:1,他引:8
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。 相似文献
13.
Portfolio optimization by minimizing conditional value-at-risk via nondifferentiable optimization 总被引:1,自引:0,他引:1
Churlzu Lim Hanif D. Sherali Stan Uryasev 《Computational Optimization and Applications》2010,46(3):391-415
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. 相似文献
14.
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. 相似文献
15.
Credit risk optimization with Conditional Value-at-Risk criterion 总被引:27,自引:0,他引:27
Fredrik Andersson Helmut Mausser Dan Rosen Stanislav Uryasev 《Mathematical Programming》2001,89(2):273-291
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 相似文献
16.
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. 相似文献
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Harbir Antil Sergey Dolgov Akwum Onwunta 《Numerical Linear Algebra with Applications》2023,30(3):e2481
This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or partial differential equations [PDEs]) under uncertainty. As an example, we focus on the so-called Conditional Value at Risk (CVaR), but the approach is equally applicable to other coherent risk measures. Both the full and reduced space formulations are considered. The algorithm is based on low rank tensor approximations of random fields discretized using stochastic collocation. To avoid nonsmoothness of the objective function underpinning the CVaR, we propose an adaptive strategy to select the width parameter of the smoothed CVaR to balance the smoothing and tensor approximation errors. Moreover, unbiased Monte Carlo CVaR estimate can be computed by using the smoothed CVaR as a control variate. To accelerate the computations, we introduce an efficient preconditioner for the Karush–Kuhn–Tucker (KKT) system in the full space formulation.The numerical experiments demonstrate that the proposed method enables accurate CVaR optimization constrained by large-scale discretized systems. In particular, the first example consists of an elliptic PDE with random coefficients as constraints. The second example is motivated by a realistic application to devise a lockdown plan for United Kingdom under COVID-19. The results indicate that the risk-averse framework is feasible with the tensor approximations under tens of random variables. 相似文献
19.
In this paper, we develop a stochastic programming model for economic dispatch of a power system with operational reliability and risk control constraints. By defining a severity-index function, we propose to use conditional value-at-risk (CVaR) for measuring the reliability and risk control of the system. The economic dispatch is subsequently formulated as a stochastic program with CVaR constraint. To solve the stochastic optimization model, we propose a penalized sample average approximation (SAA) scheme which incorporates specific features of smoothing technique and level function method. Under some moderate conditions, we demonstrate that with probability approaching to 1 at an exponential rate with the increase of sample size, the optimal solution of the smoothing SAA problem converges to its true counterpart. Numerical tests have been carried out for a standard IEEE-30 DC power system. 相似文献
20.
This paper presents a modified ODE-based algorithm for unconstrained optimization problems. It combines the idea of IMPBOT algorithm with nonmonotone and subspace techniques. The main feature of this method is that at each iteration, a lower dimensional system of linear equations is solved to obtain a trial step. Under some standard assumptions, the method is proven to be globally convergent. Numerical results show the efficiency of this proposed method in practical computation. 相似文献