An algebraic approach to integer portfolio problems

Castro, Fátima Roldán; Gago, J.; Hartillo, I.; Puerto, Justo; Ucha, J. M.

doi:10.1016/j.ejor.2010.11.007

Cited by 18 publications

(13 citation statements)

References 24 publications

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“…(22), (6), (7), (8), (23), (10), (20), (Linear investor Constraints 1) (12), (13), (14), (15), (16), (17), (25), (26). (Dual2 Constraints) The formulation above still contains bilinear terms, namely a jk σ jk , in constraint (27).…”

Section: (Linear Investor Constraints 1)mentioning

confidence: 99%

Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs

Leal

Ponce

Puerto

2020

European Journal of Operational Research

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Section: (Linear Investor Constraints 1)mentioning

confidence: 99%

Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs

Leal

Ponce

Puerto

2020

European Journal of Operational Research

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“…Anagnostopoulos and Mamanis [34] compared different multi-objective evolutionary algorithms to study a nonlinear mixed-integer three-objective problem with class and quantity limitations. Castro et al [35] proposed a mathematical algorithm based on various test sets to solve a portfolio selection model with a nonlinear constraint and integer variable.…”

Section: Introductionmentioning

confidence: 99%

A portfolio selection model based on the knapsack problem under uncertainty

2019

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One of the primary concerns in investment planning is to determine the number of shares for asset with relatively high net value of share such as Berkshire Hathaway on Stock market. Traditional asset allocation methods like Markowitz theorem gives the solution as a percentage and this ratio may suggest allocation of half of a share on the market, which is impractical. Thus, it is necessary to propose a method to determine the number of shares for each asset. This paper presents a knapsack based portfolio selection model where the expected returns, prices, and budget are characterized by interval values. The study determines the priority and importance of each share in the proposed model by extracting the interval weights from an interval comparison matrix. The resulted model is converted into a parametric linear programming model in which the decision maker is able to determine the optimism threshold. Finally, a discrete firefly algorithm is designed to find the near optional solutions in large dimensions. The proposed study is implemented for some data from the US stock exchange.

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“…To the best of our knowledge, there have been few practical examples where the walk-back procedure has been successfully applied, as in [30], [17], [9]. This lack of applicability may be due to its two main drawbacks: the computation of the test set and the time required for visiting the points x ∈ A to eventually obtain an optimum for (P).…”

Section: 3mentioning

confidence: 99%

An improved test set approach to nonlinear integer problems with applications to engineering design

et al. 2015

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Abstract. Many problems in engineering design involve the use of nonlinearities and some integer variables. Methods based on test sets have been proposed to solve some particular problems with integer variables, but they have not been frequently applied because of computation costs. The walk-back procedure based on a test set gives an exact method to obtain an optimal point of an integer programming problem with linear and nonlinear constraints, but the calculation of this test set and the identification of an optimal solution using the test set directions are usually computationally intensive.In problems for which obtaining the test set is reasonably fast, we show how the effectiveness can still be substantially improved. This methodology is presented in its full generality and illustrated on two specific problems: (1) minimizing cost in the problem of scheduling jobs on parallel machines given restrictions on demands and capacity, and (2) minimizing cost in the series parallel redundancy allocation problem, given a target reliability. Our computational results are promising and suggest the applicability of this approach to deal with other problems with similar characteristics or to combine it with mainstream solvers to certify optimality.Non-linear Integer Programming and test set and Gröbner basis and chance constrained programming

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An algebraic approach to integer portfolio problems

Cited by 18 publications

References 24 publications

Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs

Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs

A portfolio selection model based on the knapsack problem under uncertainty

An improved test set approach to nonlinear integer problems with applications to engineering design

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