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Portfolio selection under possibilistic mean-variance utility and a SMO algorithm

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第2期197卷 693-700页

作者： Zhang, Wei-Guo Zhang, Xi-Li Xiao, Wei-Lin S China Univ Technol Sch Business Adm Guangzhou 510641 Peoples R China

In this paper, we propose a new portfolio selection model with the maximum utility based on the interval-valued possibilistic mean and possibilistic variance, which is a two-parameter quadratic programming problem. We also present a sequential minimal optimization (SMO) algorithm to obtain the optimal portfolio. The remarkable feature of the algorithm is that it is extremely easy to implement, and it can be extended to any size of portfolio selection problems for finding an exact optimal solution. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Possibilistic distribution Portfolio selection Mean-variance utility parametric quadratic programming Sequential minimal optimization (SMO)

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NUMERICAL SIMULATION OF TWO-POINT CONTACT BETWEEN WHEEL AND RAIL

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Acta Mechanica Solida Sinica 2009年第4期22卷 352-359页

作者： Jun Zhang Shouguang Sun Xuesong Jin School of Transportation Engineering Dalian Jiaotong University Dalian 116028 China School of Mechanical Electronic and Control Engineering Beijing Jiaotong University Beijing 100044 China

The elastic-plastic contact problem with rolling friction of wheel-rail is solved using the FE parametric quadratic programming method. Thus, the complex elastic-plastic contact problem can be calculated with high accuracy and efficiency, while the Hertz＇s hypothesis and the elastic semi-space assumption are avoided. Based on the ‘one-point＇ contact calculation of wheel-rail, the computational model of ‘two-point＇ contact are established and calculated when the wheel flange is close to the rail. In the case of ‘two-point＇ contact, the changing laws of wheelrail contact are introduced and contact forces in various load cases are carefully analyzed. The main reason of wheel flange wear and rail side wear is found. Lubrication computational model of the wheel flange is constructed. Comparing with the result without lubrication, the contact force between wheel flange and rail decreases, which is beneficial for reducing the wear of wheel-rail.

关键词： wheel-rail contact FEM parametric quadratic programming lubrication

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Comparative issues in large-scale mean-variance efficient frontier computation

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DECISION SUPPORT SYSTEMS 2011年第2期51卷 250-255页

作者： Steuer, Ralph E. Qi, Yue Hirschberger, Markus Univ Georgia Terry Coll Business Athens GA 30602 USA Nankai Univ Dept Financial Management Coll Business Tianjin 300071 Peoples R China Univ Eichstatt Ingolstadt Dept Math Eichstatt Germany

One of the functions of a portfolio management system is to return quickly an efficient frontier. However, in the large-scale problems (1000 to 3000 securities) that are beginning to appear with greater frequency, the task of computing the mean-variance efficient frontier, even when all constraints are linear, can range from the significant to the prohibitive. For ease of reference, we call mean-variance problems with all linear constraints Markowitz problems. With little on the time to compute a Markowitz-problem efficient frontier in the literature, we conduct experiments that involve varying problem sizes, methods employed, and optimizers used to present an overall picture of the situation and establish benchmarks in the large-scale arena. One of the conclusions of the experiments is the superiority of the class of techniques that would fall under the title of parametric quadratic programming. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Mean-variance efficient frontiers Portfolio selection Hyperbolic segments e-Constraint method parametric quadratic programming

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A dynamic programming approach to solve efficient frontier

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2004年第2期60卷 203-214页

作者： Sadjadi, SJ Aryanezhad, MB Moghaddam, BF Iran Univ Sci & Technol Dept Ind Engn Tehran Iran

This paper presents a closed form solution of the mean-variance portfolio selection problem for uncorrelated assets that precludes short sells. We also study the problem with the consideration of transaction cost. When the asset holding can be explicitly become available, one can have a better understanding of the behavior of efficient frontier. Our algorithm solves the mean-variance portfolio selection with uncorrelated risky assets plus one risk free asset. The algorithm is based on a continuous dynamic programming and provides a general closed form solution that is a function of expected returns and variances of all assets. The implementation of the algorithm is presented by some practical examples.

关键词： dynamic programming efficient frontier parametric quadratic programming

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Portfolio selection and transactions costs

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2003年第1期24卷 95-116页

作者： Best, MJ Hlouskova, J Univ Waterloo Dept Combinator & Optimizat Waterloo ON N2L 3G1 Canada Inst Adv Studies Dept Econ & Finance A-1060 Vienna Austria

This paper deals with the portfolio selection problem of risky assets with a diagonal covariance matrix, upper bounds on all assets and transactions costs. An algorithm for its solution is formulated which terminates in a number of iterations that is at most three times the number of assets. The efficient portfolios, under appropriate assumptions, are shown to have the following structure. As the risk tolerance parameter increases, an asset's holdings increases to its target, then stays there for a while, then increases to its upper bound, reaches it and stays there. Then the holdings of the asset with the next highest expected return proceeds in a similar way and so on.

关键词： parametric quadratic programming portfolio optimization transactions costs

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Value of information in portfolio selection, with a Taiwan stock market application illustration

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第2期253卷 418-427页

作者： Kao, Chiang Steuer, Ralph E. Natl Cheng Kung Univ Dept Ind & Informat Management Tainan 70101 Taiwan Univ Georgia Dept Finance Athens GA 30602 USA

Despite many proposed alternatives, the predominant model in portfolio selection is still mean-variance. However, the main weakness of the mean-variance model is in the specification of the expected returns of the individual securities involved. If this process is not accurate, the allocations of capital to the different securities will in almost all certainty be incorrect. If, however, this process can be made accurate, then correct allocations can be made, and the additional expected return following from this is the value of information. This paper thus proposes a methodology to calculate the value of information. A related idea of a level of disappointment is also shown. How value of information calculations can be important in helping a mutual fund settle on how much to set aside for research is discussed in reference to a Taiwan Stock Exchange illustrative application in which the value of information appears to be substantial. Heavy use is made of parametric quadratic programming to keep computation times down for the methodology. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Efficient points Portfolio selection Value of information Piecewise linear paths parametric quadratic programming

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Global and local quadratic minimization

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JOURNAL OF GLOBAL OPTIMIZATION 1997年第1期10卷 77-90页

作者： Best, MJ Ding, B UNIV WATERLOO DEPT COMBINATOR & OPTIMIZAT WATERLOO ON N2L 3G1 CANADA

We present a method which when applied to certain non-convex QP will locate the global minimum, all isolated local minima and some of the non-isolated local minima. The method proceeds by formulating a (multi) parametric convex QP in terms of the data of the given non-convex QP. Based on the solution of the parametric QP, an unconstrained minimization problem is formulated. This problem is piece-wise quadratic. A key result is that the isolated local minimizers (including the global minimizer) of the original non-convex problem are in one-to-one correspondence with those of the derived unconstrained problem. The theory is illustrated with several numerical examples. A numerical procedure is developed for a special class of non-convex QP's. It is applied to a problem from the literature and verifies a known global optimum and in addition, locates a previously unknown local minimum.

关键词： global optimization parametric quadratic programming non-convex quadratic program

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Fully Decentralized Optimal Power Flow of Multi-Area Interconnected Power Systems Based on Distributed Interior Point Method

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第1期33卷 901-910页

作者： Lu, Wentian Liu, Mingbo Lin, Shunjiang Li, Licheng South China Univ Technol Sch Elect Power Engn Guangzhou 510640 Guangdong Peoples R China

Traditionally, the optimal power flow (OPF) problem is solved in a centralized manner. However, with continuous expansion of the scale of multi-area interconnected power systems, realistic applications of the centralized method face additional challenges. In this paper, we propose a fully decentralized OPF algorithm for multi-area interconnected power systems based on the distributed interior point method, where solving the regional correction equation was converted into solving a parametric quadratic programming problem during each Newton-Raphson iteration. This is a novel approach to tackle the decentralized OPF problems. We analyzed the convergence property of this algorithm. The proposed approach is fully decentralized without central coordinator and parameter tuning, and is robust to network partitioning. Furthermore, this decentralized algorithm enjoys the same convergence performance and accuracy as the centralized interior point method. Results on a 3-bus test system, 4 IEEE test systems, and a real 4-area 6056-bus interconnected system show the benefits of the proposed method.

关键词： Decentralized optimization distributed interior point method multi-area interconnected power system optimal power flow parametric quadratic programming

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A note on the kinks at the mean variance frontier

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1999年第1期112卷 236-239页

作者： Voros, J Kriens, J Strijbosch, LWG Janus Pannonius Univ Fac Business & Econ Dept Management Sci Pecs Hungary Tilburg Univ NL-5000 LE Tilburg Netherlands

In this paper the standard portfolio case with short sales restrictions is analyzed. Dybvig pointed out that if there is a kink at a risky portfolio on the efficient frontier, then the securities in this portfolio have equal expected return and the converse of this statement is false. For the existence of kinks at the efficient frontier the sufficient condition is given here and a new procedure is used to derive the efficient frontier, i.e. the characteristics of the mean variance frontier. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： portfolio analysis parametric quadratic programming

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Extracting from the relaxed for large-scale semi-continuous variable nondominated frontiers

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JOURNAL OF GLOBAL OPTIMIZATION 2016年第1期64卷 33-48页

作者： Steuer, Ralph E. Hirschberger, Markus Deb, Kalyanmoy Univ Georgia Dept Finance Athens GA 30602 USA Munich Re D-80802 Munich Germany Michigan State Univ Coll Engn E Lansing MI 48824 USA

Because of size and covariance matrix problems, computing much of anything along the nondominated frontier of a large-scale (1000-3000 securities) portfolio selection problem with semi-continuous variables is a task that has not previously been achieved. But given (a) the speed at which the nondominated frontier of a classical portfolio problem can now be computed and (b) the possibility that there might be overlaps between the nondominated frontier of the classical problem and that of the same problem but with semi-continuous variables, the paper shows how considerable amounts of the nondominated frontier of a large-scale mean-variance portfolio selection problem with semi-continuous variables can be computed in very little time.

关键词： Multiple criteria optimization Portfolio selection Buy-in thresholds Nondominated frontiers Semi-continuous variables parametric quadratic programming

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