Ant Colony Optimization for Markowitz Mean-Variance Portfolio Model

Deng, Guang-Feng; Lin, Woo-Tsong

doi:10.1007/978-3-642-17563-3_29

Cited by 30 publications

(15 citation statements)

References 10 publications

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“…Bienstock (1996) (see also Shaw et al, 2008) shows that problem (1) with cardinality constraint (16) is NP-hard, even when r = 3. Several authors (see, e.g., Chang et al, 2000;Fernández and Gómez, 2007;Soleimani et al, 2009;Deng and Lin, 2010;Woodside-Oriakhi et al, 2011) consider an equality version for cardinality constraint (16) and propose mainly heuristic methods to solve the corresponding problem:…”

Section: Cardinality Constraintsmentioning

confidence: 99%

“…Bienstock () (see also Shaw et al., ) shows that problem (1) with cardinality constraint is NP‐hard, even when

r = 3

. Several authors (see, e.g., Chang et al., ; Fernández and Gómez, ; Soleimani et al., ; Deng and Lin, ; Woodside‐Oriakhi et al., ) consider an equality version for cardinality constraint and propose mainly heuristic methods to solve the corresponding problem:

0true \sum_{j = 1}^{r} δ_{j} = \bar{K} .

Moreover, finding the

\bar{K}

assets that should be included in the optimal portfolio is, in general, an NP‐hard problem (Moral‐Escudero et al., ).…”

Section: Additional Constraintsmentioning

confidence: 99%

See 1 more Smart Citation

Complex portfolio selection via convex mixed‐integer quadratic programming: a survey

Mencarelli

d'Ambrosio

2018

Int Trans Operational Res

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In this paper, we review convex mixed-integer quadratic programming approaches to deal with single-objective single-period mean-variance portfolio selection problems under real-world financial constraints. In the first part, after describing the original Markowitz's mean-variance model, we analyze its theoretical and empirical limitations, and summarize the possible improvements by considering robust and probabilistic models, and additional constraints. Moreover, we report some recent theoretical convexity results for the probabilistic portfolio selection problem. In the second part, we overview the exact algorithms proposed to solve the single-objective single-period portfolio selection problem with quadratic risk measure.

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Section: Cardinality Constraintsmentioning

confidence: 99%

“…Bienstock () (see also Shaw et al., ) shows that problem (1) with cardinality constraint is NP‐hard, even when

r = 3

0true \sum_{j = 1}^{r} δ_{j} = \bar{K} .

Moreover, finding the

\bar{K}

assets that should be included in the optimal portfolio is, in general, an NP‐hard problem (Moral‐Escudero et al., ).…”

Section: Additional Constraintsmentioning

confidence: 99%

Complex portfolio selection via convex mixed‐integer quadratic programming: a survey

Mencarelli

d'Ambrosio

2018

Int Trans Operational Res

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show abstract

“…Several authors (see, e.g., [49,70,87,229,243]) consider an equality version for cardinality constraint (3.16) and propose mainly heuristic methods to solve the corresponding problem:…”

Section: Cardinality Constraintsmentioning

confidence: 99%

The multiplicative weights update algorithm for mixed integer nonlinear programming: theory, applications, and limitations

Mencarelli

2018

4OR-Q J Oper Res

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“…Some metaheuristics based approaches are also used such as simulated annealing [4], genetic algorithm [5], particle swarm optimization [6], ant colony optimization [7]. In [20] authors had discussed about some advanced optimization techniques.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Programming Approach to Multi-objective Mean Variance Model

Islam¹,

Chaudhury²

2017

APAM

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Abstract. The traditional single objective mean variance optimization model fails to satisfy the investors with multiple investment objectives. So multi-objective portfolio optimization model is considered in this paper. Since this will help investors to achieve highest expected return among the different financial products of the capital market and to fulfill the expected return objectives simultaneously. Fuzzy Non-Linear Programming (FNLP) and Fuzzy Additive Goal Programming (FAGP) techniques are used to solve this multi-objective model. Since it will fulfill the wanted aspiration level of the investors concerning return and risk objectives. And finally solution procedure is illustrated by numerical examples.

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Ant Colony Optimization for Markowitz Mean-Variance Portfolio Model

Cited by 30 publications

References 10 publications

Complex portfolio selection via convex mixed‐integer quadratic programming: a survey

Complex portfolio selection via convex mixed‐integer quadratic programming: a survey

The multiplicative weights update algorithm for mixed integer nonlinear programming: theory, applications, and limitations

A Fuzzy Programming Approach to Multi-objective Mean Variance Model

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