Portfolio optimization with an envelope-based multi-objective evolutionary algorithm

Branke, Jürgen; Scheckenbach, Benedikt; Stein, Michael; Deb, Kalyan; Schmeck, Hartmut

doi:10.1016/j.ejor.2008.01.054

Cited by 169 publications

(86 citation statements)

References 14 publications

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“…This type of domain appears in portfolio optimization problems with buy-in thresholds [5]. Note that it is allowed to choose all D i differently, so that Problem (1) also contains the mixed-integer case.…”

Section: The New Approachmentioning

confidence: 99%

Semidefinite relaxations for non-convex quadratic mixed-integer programming

Buchheim

Wiegele

2012

Math. Program.

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Abstract. We present semidefinite relaxations for unconstrained nonconvex quadratic mixed-integer optimization problems. These relaxations yield tight bounds and are computationally easy to solve for mediumsized instances, even if some of the variables are integer and unbounded. In this case, the problem contains an infinite number of linear constraints; these constraints are separated dynamically. We use this approach as a bounding routine in an SDP-based branch-and-bound framework. In case of a convex objective function, the new SDP bound improves the bound given by the continuous relaxation of the problem. Numerical experiments show that our algorithm performs well on various types of non-convex instances.

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Section: The New Approachmentioning

confidence: 99%

Semidefinite relaxations for non-convex quadratic mixed-integer programming

Buchheim

Wiegele

2012

Math. Program.

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“…The objective function minimizes the expected return by considering budget constrain. For more details, please see Chang et al (2000), Branke et al (2009) and Soleimani et al (2009). The proposed model has been applied on monthly information gathered from Tehran Stock Exchange by considering Covariance between stock returns and mentioned industries, budget, investor optimum efficiency, free float stock, etc.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The explained that the new model could be formulated as an Np-Hard problem and they proposed a genetic algorithm to solve the resulted model. Branke et al (2009) proposed to combined an active set algorithm optimized for portfolio selection into a multi-objective evolutionary algorithm (MOEA). The idea was to let the MOEA come up with some convex subsets of the set of all possible portfolios, solve a critical line algorithm for each subset, and then merge the partial solutions into a solution of the original non-convex problem.…”

Section: Introductionmentioning

confidence: 99%

An application of Markowitz theorem on Tehran Stock Exchange

Ghodrati¹,

Mohammad²

2014

10.5267/j.msl

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During the past 65 years, there have been tremendous efforts on portfolio selection problem. The standard Markowitz mean-variance model to portfolio selection includes tracing out an efficient frontier, a continuous curve demonstrating the tradeoff between return and risk. This frontier can be often detected via standard quadratic programming, categorized in convex optimization. Traditional Markowitz problem has been recently extended into a new form of mixed integer nonlinear problems by considering various constraints such as cardinality constraints, industry limitation, etc. This paper proposes a mixed integer nonlinear programming to determine optimal asset allocation on Tehran Stock Exchange. The results have indicated that a petrochemical firm named Farabi has gained 44% of the portfolio followed by a drug firm named Kosar Pharmacy gaining 28%. In addition, banking sector was the third winning firm where Eghtesad Novin bank gained nearly 10% of the portfolio. Minerals and mining firms were the next sector in our portfolio where Gol Gohar Iron Ore and Tehran Cement collected 0.73% and 0.57% of the portfolio, respectively. In our survey, auto industry gained only 0.26% of the portfolio, which belonged to Saipa group.

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“…To avoid this problem researchers define a constraint named cardinality. Cardinality is considered as a constraint in many researches such as: Gupta et al (2008), Chang et al (2009), Branke et al (2009), Golmakani & Fazel (2011), Yang et al (2011, Anagnostopoulos & Mamanis (2011) and Woodside-Oriakhi et al (2011). Anagnostopoulos & Mamanis (2010) proposed cardinality as an objective function that should be minimized.…”

Section: Introductionmentioning

confidence: 99%

A Two-Stage Method for Considering Cardinality in Portfolio Optimization of Mutual Funds

Alimi¹

2015

MAS

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Mutual funds are important financial institutes. There are several methods for performance evaluation of mutual funds such as portfolio optimization. Portfolio optimization has a basic model that has completed up to now. One of completions is adding cardinality constraint to the model. Considering cardinality in portfolio optimization model makes it an integer programming problem that solving it, is hard and makes the efficient frontier discontinuous. In current study in first stage we rank the mutual funds with VIKOR method and based on 5 characteristics: rate of return, variance, semivariance, Treynor ratio and Sharpe ratio. In second stage according to cardinality level best ranked mutual funds are chosen. A mean-semivariance portfolio optimization model is written using chosen funds. This model is solved using fuzzy technique programming and efficient frontier is obtained. Real data from NASDAQ based on 92 mutual funds are used to illustrate the effectiveness of proposed methodology. Results show that the efficient frontier obtained from our methodology is continuous and near to unconstrained efficient frontier.

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Portfolio optimization with an envelope-based multi-objective evolutionary algorithm

Cited by 169 publications

References 14 publications

Semidefinite relaxations for non-convex quadratic mixed-integer programming

Semidefinite relaxations for non-convex quadratic mixed-integer programming

An application of Markowitz theorem on Tehran Stock Exchange

A Two-Stage Method for Considering Cardinality in Portfolio Optimization of Mutual Funds

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