Computation of mean-semivariance efficient sets by the Critical Line Algorithm

Markowitz, Harry M.; Todd, Peter A.; Xu, Ganlin; Yamane, Yuji

doi:10.1007/bf02282055

Cited by 159 publications

(71 citation statements)

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“…Similarly, Grootveld and Hallerbach (1999) generate mean-LPM efficient frontiers and state that the numerical optimization process they use for solving the problem in Equations (10) and (11) is tedious and demanding, but do not provide details of such process. Markowitz et al (1993) transform the mean-semivariance problem into a quadratic problem by adding fictitious securities. This modification enables them to apply to the modified mean-semivariance problem the critical line algorithm originally developed to solve the mean-variance problem.…”

Section: E Some Possible Solutionsmentioning

confidence: 99%

Mean-Semivariance Optimization: A Heuristic Approach

Estrada

2007

SSRN Journal

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Section: E Some Possible Solutionsmentioning

confidence: 99%

Mean-Semivariance Optimization: A Heuristic Approach

Estrada

2007

SSRN Journal

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“…Besides, variance counts both upward and downward deviation, which is contrary to the definition of investment risk. Later, to supply the gap, Markowitz [5] replaces the risk measure with the semi-variance, which only counts downward deviation. In addition, Konno [6] and Speranza [7] introduce the mean absolute deviation (MAD) into portfolio optimization model as risk measure.…”

Section: Introductionmentioning

confidence: 99%

Gray Wolf Optimization Algorithm for Multi-Constraints Second-Order Stochastic Dominance Portfolio Optimization

et al. 2018

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Abstract:In the field of investment, how to construct a suitable portfolio based on historical data is still an important issue. The second-order stochastic dominant constraint is a branch of the stochastic dominant constraint theory. However, only considering the second-order stochastic dominant constraints does not conform to the investment environment under realistic conditions. Therefore, we added a series of constraints into basic portfolio optimization model, which reflect the realistic investment environment, such as skewness and kurtosis. In addition, we consider two kinds of risk measures: conditional value at risk and value at risk. Most important of all, in this paper, we introduce Gray Wolf Optimization (GWO) algorithm into portfolio optimization model, which simulates the gray wolf's social hierarchy and predatory behavior. In the numerical experiments, we compare the GWO algorithm with Particle Swarm Optimization (PSO) algorithm and Genetic Algorithm (GA). The experimental results show that GWO algorithm not only shows better optimization ability and optimization efficiency, but also the portfolio optimized by GWO algorithm has a better performance than FTSE100 index, which prove that GWO algorithm has a great potential in portfolio optimization.

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“…Markowitz (1959) defined a semi-variance for as symmetric random returns since researchers pointed out that the asymmetric returns is not an appropriate method for measuring the risk. Many researchers studied the properties and computation problem about semi-variance (Grootveld & Hallerbach, 1999;Markowitz, 1993) and developed the mean-semivariance models (Chow & Denning, 1994). Konno and Yamazaki (1991) introduced an advanced model in which a mean-absolute deviation (MAD) model and absolute deviation were utilized as a measure of risk.…”

Section: Introductionmentioning

confidence: 99%

Possibility theory for multiobjective fuzzy random portfolio optimization

Sadati¹,

Doniavi²,

Samadi³

2014

10.5267/j.dsl

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The problem of portfolio optimization is a standard problem in financial world and it has received tremendous attentions. Portfolio optimization plays essential role in determining portfolio strategies for investors. Portfolio optimization is intrinsically a discrete optimization problem whose decision criteria are in conflict and the proposed study of this paper considers a portfolio optimization problem involving fuzzy random variables. To solve the proposed model, we first present the possibility and necessity-based model to reformulate the fuzzy random portfolio selection model into linear programming models and using the resulted linear programs, a multi-objective problem is constructed. To solve the multi-objective problem we propose some methods to consider decision makers' optimistic and pessimistic views. A numerical example illustrates the whole idea on multiobjective fuzzy random portfolio optimization by possibility and necessity-based model.

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Computation of mean-semivariance efficient sets by the Critical Line Algorithm

Cited by 159 publications

References 1 publication

Mean-Semivariance Optimization: A Heuristic Approach

Mean-Semivariance Optimization: A Heuristic Approach

Gray Wolf Optimization Algorithm for Multi-Constraints Second-Order Stochastic Dominance Portfolio Optimization

Possibility theory for multiobjective fuzzy random portfolio optimization

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