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1.
The original Markowitz model of portfolio selection has received a widespread theoretical acceptance and it has been the basis for various portfolio selection techniques. Nevertheless, this normative model has found relatively little application in practice when some additional features, such as fixed costs and minimum transaction lots, are relevant in the portfolio selection problem. In this paper different mixed-integer linear programming models dealing with fixed costs and possibly minimum lots are introduced. Due to the high computational complexity of the models, heuristic procedures, based on the construction and optimal solution of mixed integer subproblems, are proposed. Computational results obtained using data from the Milan Stock Exchange show how the proposed heuristics yield very good solutions in a short computational time and make possible some interesting financial conclusions on the impact of fixed costs and minimum lots on portfolio composition. 相似文献
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J. Branke B. Scheckenbach M. Stein K. Deb H. Schmeck 《European Journal of Operational Research》2009,199(3):684-693
The problem of portfolio selection is a standard problem in financial engineering and has received a lot of attention in recent decades. Classical mean–variance portfolio selection aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance. In the case of linear constraints, the problem can be solved efficiently by parametric quadratic programming (i.e., variants of Markowitz’ critical line algorithm). However, there are many real-world constraints that lead to a non-convex search space, e.g., cardinality constraints which limit the number of different assets in a portfolio, or minimum buy-in thresholds. As a consequence, the efficient approaches for the convex problem can no longer be applied, and new solutions are needed.In this paper, we propose to integrate an active set algorithm optimized for portfolio selection into a multi-objective evolutionary algorithm (MOEA). The idea is to let the MOEA come up with some convex subsets of the set of all feasible portfolios, solve a critical line algorithm for each subset, and then merge the partial solutions to form the solution of the original non-convex problem. We show that the resulting envelope-based MOEA significantly outperforms existing MOEAs. 相似文献
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Simulated annealing for complex portfolio selection problems 总被引:2,自引:0,他引:2
This paper describes the application of a simulated annealing approach to the solution of a complex portfolio selection model. The model is a mixed integer quadratic programming problem which arises when Markowitz’ classical mean–variance model is enriched with additional realistic constraints. Exact optimization algorithms run into difficulties in this framework and this motivates the investigation of heuristic techniques. Computational experiments indicate that the approach is promising for this class of problems. 相似文献
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This paper considers an asset-liability management (ALM) problem under a continuous-time Markov regime-switching model. By adopting the techniques of [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model. SIAM J. Control Optim. 42, 1466-1482], we investigate the feasibility, obtain the optimal strategy, delineate the efficient frontier, and establish the associated mutual fund theorem. 相似文献
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Markowitz的均值-方差模型在投资组合优化中得到了广泛的运用和拓展,其中多数拓展模型仅局限于对随机投资组合或模糊投资组合的研究,而忽略了实际问题同时包含了随机信息和模糊信息两个方面。本文首先定义随机模糊变量的方差用以度量投资组合的风险,提出具有阀值约束的最小方差随机模糊投资组合模型,基于随机模糊理论,将该模型转化为具有线性等式和不等式约束的凸二次规划问题。为了提高上述模型的有效性,本文以投资者期望效用最大化为压缩目标对投资组合权重进行压缩,构建等比例-最小方差混合的随机模糊投资组合模型,并求解该模型的最优解。最后,运用滚动实际数据的方法,比较上述两个模型的夏普比率以验证其有效性。 相似文献
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The concepts of portfolio optimization and diversification have been instrumental in the development and understanding of financial markets and financial decision making. In light of the 60 year anniversary of Harry Markowitz’s paper “Portfolio Selection,” we review some of the approaches developed to address the challenges encountered when using portfolio optimization in practice, including the inclusion of transaction costs, portfolio management constraints, and the sensitivity to the estimates of expected returns and covariances. In addition, we selectively highlight some of the new trends and developments in the area such as diversification methods, risk-parity portfolios, the mixing of different sources of alpha, and practical multi-period portfolio optimization. 相似文献
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Renata Mansini Wlodzimierz Ogryczak M. Grazia Speranza 《European Journal of Operational Research》2014
Markowitz formulated the portfolio optimization problem through two criteria: the expected return and the risk, as a measure of the variability of the return. The classical Markowitz model uses the variance as the risk measure and is a quadratic programming problem. Many attempts have been made to linearize the portfolio optimization problem. Several different risk measures have been proposed which are computationally attractive as (for discrete random variables) they give rise to linear programming (LP) problems. About twenty years ago, the mean absolute deviation (MAD) model drew a lot of attention resulting in much research and speeding up development of other LP models. Further, the LP models based on the conditional value at risk (CVaR) have a great impact on new developments in portfolio optimization during the first decade of the 21st century. The LP solvability may become relevant for real-life decisions when portfolios have to meet side constraints and take into account transaction costs or when large size instances have to be solved. In this paper we review the variety of LP solvable portfolio optimization models presented in the literature, the real features that have been modeled and the solution approaches to the resulting models, in most of the cases mixed integer linear programming (MILP) models. We also discuss the impact of the inclusion of the real features. 相似文献
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This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that
future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities
and decision makers’ predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility
to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit
and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are
formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic
equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between
the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems
and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a
portfolio selection problem is provided to compare our proposed models with the basic model. 相似文献
9.
This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio’s worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifying the optimal terminal wealth distribution and a stochastic linear programming model replicating the identified optimal portfolio wealth. The replicating portfolio coincides with the optimal solution to the investor’s problem if the market is frictionless. The multiperiod stochastic linear programming model tests for the absence of arbitrage opportunities and its dual feasible solutions generate all risk neutral probability measures. When there are constraints such as liquidity or position requirements, the method yields approximate portfolio policies by minimizing the initial cost of the replication portfolio. A numerical example illustrates the difference between the replicating result and the optimal unconstrained portfolio. 相似文献
10.
本文研究考虑交易成本的投资组合模型,分别以风险价值(VAR)和夏普比率(SR)作为投资组合的风险评价指标和效益评价指标。为有效求解此模型,本文在引力搜索和粒子群算法的基础上提出了一种混合优化算法(IN-GSA-PSO),将粒子群算法的群体最佳位置和个体最佳位置与引力搜索算法的加速度算子有机结合,使混合优化算法充分发挥单一算法的开采能力和探索能力。通过对算法相关参数的合理设置,算法能够达到全局搜索和局部搜索的平衡,快速收敛到模型的最优解。本文选取上证50股2014年下半年126个交易日的数据,运用Matlab软件进行仿真实验,实验结果显示,考虑交易成本的投资组合模型可使投资者得到更高的收益率。研究同时表明,基于PSO和GSA的混合算法在求解投资组合模型时比单一算法具有更好的性能,能够得到满意的优化结果。 相似文献
11.
Stochastic dominance relations are well studied in statistics, decision theory and economics. Recently, there has been significant
interest in introducing dominance relations into stochastic optimization problems as constraints. In the discrete case, stochastic
optimization models involving second order stochastic dominance constraints can be solved by linear programming. However,
problems involving first order stochastic dominance constraints are potentially hard due to the non-convexity of the associated
feasible regions. In this paper we consider a mixed 0–1 linear programming formulation of a discrete first order constrained
optimization model and present a relaxation based on second order constraints. We derive some valid inequalities and restrictions
by employing the probabilistic structure of the problem. We also generate cuts that are valid inequalities for the disjunctive
relaxations arising from the underlying combinatorial structure of the problem by applying the lift-and-project procedure.
We describe three heuristic algorithms to construct feasible solutions, based on conditional second order constraints, variable
fixing, and conditional value at risk. Finally, we present numerical results for several instances of a real world portfolio
optimization problem.
This research was supported by the NSF awards DMS-0603728 and DMI-0354678. 相似文献
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Włodzimierz Ogryczak 《Annals of Operations Research》2000,97(1-4):143-162
The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between
expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating
a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences
for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on
expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does
not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection
problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model
of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless,
it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown
that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques
applied to our multiple criteria model.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
17.
A review of credibilistic portfolio selection 总被引:1,自引:0,他引:1
Xiaoxia Huang 《Fuzzy Optimization and Decision Making》2009,8(3):263-281
This paper reviews the credibilistic portfolio selection approaches which deal with fuzzy portfolio selection problem based
on credibility measure. The reason for choosing credibility measure is given. Several mathematical definitions of risk of
an investment in the portfolio are introduced. Some credibilistic portfolio selection models are presented, including mean-risk
model, mean-variance model, mean-semivariance model, credibility maximization model, α-return maximization model, entropy optimization model and game models. A hybrid intelligent algorithm for solving the optimization
models is documented. In addition, as extensions of credibilistic portfolio selection approaches, the paper also gives a brief
review of some hybrid portfolio selection models. 相似文献
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带交易费用的投资组合模型的割平面解法 总被引:2,自引:0,他引:2
本文讨论了带交易费用的投资组合模型,因对这一类带二次约束的线性优化问题没有特殊的处理方法,我们利用割平面法使这一非线性优化间题可通过解一系列线性规划问题来求解. 相似文献
19.
目前,在Markowitz的均值-方差模型基础上对含有偏度和交易成本模型的研究较少,结合国内市场数据进行研究并做出三维投资组合有效前沿图像的成果更少。在建立两种在交易成本约束条件下以方差和偏度的线性组合为目标函数的最优投资组合模型之后,利用线性函数逼近,将模型转换成线性规划问题,而且这种逼近程度可以控制。用单纯形法求解以得到最优投资组合。利用国内八个上市公司的数据进行实证分析,做出了三维投资组合近似有效前沿图像,并讨论了目标函数最优值和参数的关系。可以发现,目标函数是期望r和参数m的增函数。 相似文献
20.
Florian Kellner Bernhard Lienland Sebastian Utz 《European Journal of Operational Research》2019,272(2):505-522
This research presents a novel, state-of-the-art methodology for solving a multi-criteria supplier selection problem considering risk and sustainability. It combines multi-objective optimization with the analytic network process to take into account sustainability requirements of a supplier portfolio configuration. To integrate ‘risk’ into the supplier selection problem, we develop a multi-objective optimization model based on the investment portfolio theory introduced by Markowitz. The proposed model is a non-standard portfolio selection problem with four objectives: (1) minimizing the purchasing costs, (2) selecting the supplier portfolio with the highest logistics service, (3) minimizing the supply risk, and (4) ordering as much as possible from those suppliers with outstanding sustainability performance. The optimization model, which has three linear and one quadratic objective function, is solved by an algorithm that analytically computes a set of efficient solutions and provides graphical decision support through a visualization of the complete and exactly-computed Pareto front (a posteriori approach). The possibility of computing all Pareto-optimal supplier portfolios is beneficial for decision makers as they can compare all optimal solutions at once, identify the trade-offs between the criteria, and study how the different objectives of supplier portfolio configuration may be balanced to finally choose the composition that satisfies the purchasing company's strategy best. The approach has been applied to a real-world supplier portfolio configuration case to demonstrate its applicability and to analyze how the consideration of sustainability requirements may affect the traditional supplier selection and purchasing goals in a real-life setting. 相似文献