资产组合鲁棒优化模型及应用研究

本文在对资产组合鲁棒优化理论归纳总结的基础上,根据我国实际情况,考虑未来经济因素的不确定性,建立了相应的资产组合鲁棒优化模型。对基金公司的投资决策、银行卡网络资金分配、VaR约束下的资产组合选择等实际问题进行了研究。针对每一个具体问题,调整和改进了模型的目标函数和约束条件,用相应的不确定集描述有关的未来不确定经济因素,得到了鲁棒优化结果,使得资产组合决策兼具可行性和最优性。     

鲁棒均值-CVaR投资组合模型及实证:基于安全准则的视角

考虑证券市场的不确定性,将资产的收益率看成区间随机变量。利用鲁棒优化方法,构建鲁棒均值-CVaR投资组合模型。采用对偶理论,将鲁棒均值-CVaR投资组合模型转换为线性规划问题,降低了模型的求解难度,有助于计算大规模的资产组合。进一步地,考虑投资者的安全性需求,在模型中引入最大违反概率,控制模型的保守程度,并直观反映投资者的安全性要求。采用实证的方法,研究模型的有效性。结果表明:鲁棒均值-CVaR投资组合模型具有较好的稳健性,且满足投资者的安全性要求,在实际的投资决策中具有可行性。     

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.     

非对称不确定投资组合问题的鲁棒优化模型(英文)

本文研究了一类回报率不确定的投资组合问题.利用鲁棒优化方法,提出了一种鲁棒平均绝对偏差模型.现有的研究通常假设回报率是呈对称分布的不确定数据,本文提出的模型可处理非对称分布的不确定数据,适用范围更广.     

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.     

基于鲁棒二阶随机占优的投资组合优化模型研究

本文主要考虑一类经典的含有二阶随机占优约束的投资组合优化问题,其目标为最大化期望收益,同时利用二阶随机占优约束度量风险,满足期望收益二阶随机占优预定的参考目标收益。与传统的二阶随机占优投资组合优化模型不同,本文考虑不确定的投资收益率,并未知其精确的概率分布,但属于某一不确定集合,建立鲁棒二阶随机占优投资组合优化模型,借助鲁棒优化理论,推导出对应的鲁棒等价问题。最后,采用S&P 500股票市场的实际数据,对模型进行不同训练样本规模和不确定集合下的最优投资组合的权重、样本内和样本外不确定参数对期望收益的影响的分析。结果表明,投资收益率在最新的历史数据规模下得出的投资策略,能够获得较高的样本外期望收益,对未来投资更具参考意义。在保证样本内解的最优性的同时,也能取得较高的样本外期望收益和随机占优约束被满足的可行性。     

多目标优化问题鲁棒有效解与真有效解之间的关系

在一定条件下研究了多目标优化问题鲁棒有效解与真有效解之间的关系及鲁棒有效解的最优性条件.首先,给出多目标优化问题鲁棒弱有效解的概念,研究它与鲁棒有效解和真有效解之间的关系,举例说明了相关结果的合理性.其次,在次类凸和伪凸性假设下研究了鲁棒有效解的必要性条件和充分性条件.     

不确定信息下凸优化问题的鲁棒解刻划

该文旨在研究一类不确定性凸优化问题的鲁棒最优解.借助次微分的性质,首先引入了一类鲁棒型次微分约束品性.随后借助此约束品性,刻划了该不确定性凸优化问题的鲁棒最优解.最后建立了该不确定凸优化问题与其对偶问题之间的Wolfe型鲁棒对偶性.     

不确定信息下分式半无限优化问题的近似最优性刻画

该文研究了一类带不确定参数的多目标分式半无限优化问题。首先借助鲁棒优化方法,引入该不确定多目标分式优化问题的鲁棒对应优化模型,并借助Dinkelbach方法,将该鲁棒对应优化模型转化为一般的多目标优化问题。随后借助一种标量化方法,建立了该优化问题的标量化问题,并刻画了它们的解之间的关系。最后借助一类鲁棒型次微分约束规格,建立了该不确定多目标分式优化问题拟近似有效解的鲁棒最优性条件。     

鲁棒优化研究综述（英文）

鲁棒优化是解决数据不确定问题的有效方法,其本质是寻找对数据扰动不敏感的解.自2000年以来,鲁棒优化在理论研究和应用方面取得了蓬勃发展.本文介绍了鲁棒优化方法在理论研究方面取得的进展和主要研究结果.     

Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature

Since the pioneering work of Harry Markowitz, mean–variance portfolio selection model has been widely used in both theoretical and empirical studies, which maximizes the investment return under certain risk level or minimizes the investment risk under certain return level. In this paper, we review several variations or generalizations that substantially improve the performance of Markowitz’s mean–variance model, including dynamic portfolio optimization, portfolio optimization with practical factors, robust portfolio optimization and fuzzy portfolio optimization. The review provides a useful reference to handle portfolio selection problems for both researchers and practitioners. Some summaries about the current studies and future research directions are presented at the end of this paper.     

Recent Developments in Robust Portfolios with a Worst-Case Approach

Robust models have a major role in portfolio optimization for resolving the sensitivity issue of the classical mean–variance model. In this paper, we survey developments of worst-case optimization while focusing on approaches for constructing robust portfolios. In addition to the robust formulations for the Markowitz model, we review work on deriving robust counterparts for value-at-risk and conditional value-at-risk problems as well as methods for combining uncertainty in factor models. Recent findings on properties of robust portfolios are introduced, and we conclude by presenting our thoughts on future research directions.     

Robust portfolio asset allocation and risk measures

Many financial optimization problems involve future values of security prices, interest rates and exchange rates which are not known in advance, but can only be forecast or estimated. Several methodologies have therefore been proposed to handle the uncertainty in financial optimization problems. One such methodology is Robust Statistics, which addresses the problem of making estimates of the uncertain parameters that are insensitive to small variations. A different way to achieve robustness is provided by Robust Optimization, which looks for solutions that will achieve good objective function values for the realization of the uncertain parameters in given uncertainty sets. Robust Optimization thus offers a vehicle to incorporate an estimation of uncertain parameters into the decision making process. This is true, for example, in portfolio asset allocation. Starting with the robust counterparts of the classical mean-variance and minimum-variance portfolio optimization problems, in this paper we review several mathematical models, and related algorithmic approaches, that have recently been proposed to address uncertainty in portfolio asset allocation, focusing on Robust Optimization methodology. We also give an overview of some of the computational results that have been obtained with the described approaches. In addition we analyze the relationship between the concepts of robustness and convex risk measures.     

Robust portfolio asset allocation and risk measures

Many financial optimization problems involve future values of security prices, interest rates and exchange rates which are not known in advance, but can only be forecast or estimated. Several methodologies have therefore, been proposed to handle the uncertainty in financial optimization problems. One such methodology is Robust Statistics, which addresses the problem of making estimates of the uncertain parameters that are insensitive to small variations. A different way to achieve robustness is provided by Robust Optimization which, given optimization problems with uncertain parameters, looks for solutions that will achieve good objective function values for the realization of these parameters in given uncertainty sets. Robust Optimization thus offers a vehicle to incorporate an estimation of uncertain parameters into the decision making process. This is true, for example, in portfolio asset allocation. Starting with the robust counterparts of the classical mean-variance and minimum-variance portfolio optimization problems, in this paper we review several mathematical models, and related algorithmic approaches, that have recently been proposed to address uncertainty in portfolio asset allocation, focusing on Robust Optimization methodology. We also give an overview of some of the computational results that have been obtained with the described approaches. In addition we analyse the relationship between the concepts of robustness and convex risk measures.     

Robust portfolios that do not tilt factor exposure

Robust portfolios reduce the uncertainty in portfolio performance. In particular, the worst-case optimization approach is based on the Markowitz model and form portfolios that are more robust compared to mean–variance portfolios. However, since the robust formulation finds a different portfolio from the optimal mean–variance portfolio, the two portfolios may have dissimilar levels of factor exposure. In most cases, investors need a portfolio that is not only robust but also has a desired level of dependency on factor movement for managing the total portfolio risk. Therefore, we introduce new robust formulations that allow investors to control the factor exposure of portfolios. Empirical analysis shows that the robust portfolios from the proposed formulations are more robust than the classical mean–variance approach with comparable levels of exposure on fundamental factors.     

Using medians in portfolio optimization

Some new portfolio optimization models are formulated by adopting the sample median instead of the sample mean as the investment efficiency measure. The median is a robust statistic, which is less affected by outliers than the mean, and in portfolio models this is particularly relevant as data are often characterized by attributes such as skewness, fat tails and jumps, which may strongly bias the mean estimate. As in mean/variance optimization, the portfolio problems are formulated as finding the optimal weights, for example, wealth allocation, which maximize the portfolio median, with risk constrained by some risk measure, respectively, the Value-at-Risk, the Conditional Value-at-Risk, the Mean Absolute Deviation and the Maximum Loss, for a whole of four different models. All these models are formulated as mixed integer linear programming problems, which, at least for moderate sized problems, are efficiently solved by standard software. Models are tested on real financial data, compared to some benchmark portfolios, and found to give good results in terms of realized profits. An important feature is greater portfolio diversification than that obtained with other portfolio models.     

Robust ranking and portfolio optimization

The portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out-of-sample performance due to estimation errors in the expected returns. A practical method for portfolio construction is to use assets’ ordering information, expressed in the form of preferences over the stocks, instead of the exact expected returns. Due to the fact that the ranking itself is often described with uncertainty, we introduce a generic robust ranking model and apply it to portfolio optimization. In this problem, there are n objects whose ranking is in a discrete uncertainty set. We want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking. This robust ranking problem is a mixed integer minimax problem and is very difficult to solve in general. To solve this robust ranking problem, we apply the constraint generation method, where constraints are efficiently generated by solving a network flow problem. For empirical tests, we use post-earnings-announcement drifts to obtain ranking uncertainty sets for the stocks in the DJIA index. We demonstrate that our robust portfolios produce smaller risk compared to their non-robust counterparts.     

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.     

Robust optimization and portfolio selection: The cost of robustness

Robust optimization is a tractable alternative to stochastic programming particularly suited for problems in which parameter values are unknown, variable and their distributions are uncertain. We evaluate the cost of robustness for the robust counterpart to the maximum return portfolio optimization problem. The uncertainty of asset returns is modelled by polyhedral uncertainty sets as opposed to the earlier proposed ellipsoidal sets. We derive the robust model from a min-regret perspective and examine the properties of robust models with respect to portfolio composition. We investigate the effect of different definitions of the bounds on the uncertainty sets and show that robust models yield well diversified portfolios, in terms of the number of assets and asset weights.     

Optimal and coherent economic-capital structures: evidence from long and short-sales trading positions under illiquid market perspectives

This paper broadens research literature associated with the assessment of modern portfolio risk management techniques by presenting a thorough modeling of nonlinear dynamic asset allocation and management under the supposition of illiquid and adverse market settings. Specifically, the paper proposes a re-engineered and robust approach to optimal economic capital allocation, in a Liquidity-Adjusted Value at Risk (L-VaR) framework, and particularly from the perspective of trading portfolios that have both long and short-sales trading positions. This paper expands previous approaches by explicitly modeling the liquidation of trading portfolios, over the holding period, with the aid of an appropriate scaling of the multiple-assets’ L-VaR matrix along with GARCH-M technique to forecast conditional volatility and expected return. Moreover, in this paper, the authors develop a dynamic nonlinear portfolio selection model and an optimization algorithm which allocates both economic capital and trading assets subject to some selected financial and operational rational constraints. The empirical results strongly confirm the importance of enforcing financially and operationally meaningful nonlinear and dynamic constraints, when they are available, on economic capital optimization procedure. The empirical results are interesting in terms of theory as well as practical applications and can aid in developing robust portfolio management algorithms that financial entities could consider in light of the aftermath of the latest financial crisis.