Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems
type: Item
instance of: scholarly article
title: Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems
zbMATH Open document ID: 1471.91507
published in: Journal of Global Optimization
publication date: 2021-08-17T00:00:00Z
review text: Due to the globalization of financial markets, investors have access to thousands of financial instruments (assets). The portfolio selection problem can be modelled with the use of the famous Markowitz's mean-variance (bi-objective) model -- the mean-variance problem (MVP) -- or its extensions. However, solving large-scale cardinality-constrained Markowitz mean-variance portfolio investment problems, exact solvers may be unable to derive some efficient portfolios, even within a reasonable time limit. In such cases, information on the distance from the best feasible solution, found before the optimization process has stopped, to the true efficient solution is unavailable. Moreover, portfolio management with a large number of assets might be costly, especially when an investor makes investment decisions relatively often. In order to limit the number of assets in efficient portfolios, a cardinality constraint can be added to the MVP. This leads to the cardinality-constrained Markowitz mean-variance portfolio investment problem (CCMP). The present paper focuses is the (bi-objective) CCMP. To start with, the author recalls the bi-objective problem formulation in its most general form and also recalls a method for the derivation of efficient solutions which is instrumental for the subsequent development. Then the CCMP is formulated and some of its properties that motivate to apply so called lower and upper bounds on values of objective functions of implicit efficient solutions, are considered. Taking this into account, the author shows how to calculate the lower and upper bounds on objective function values of implicitly given efficient solutions, mentioned above, and provides a method of populating lower and upper shells to the CCMP. Chebyshev scalarization is one of the main mathematical tools. Afterwards, the theory is illustrated by demonstration how the bounds work on a large-scale instance of the CCMP when a time limit on optimization is assumed.
Mathematics Subject Classification ID: 91G10
zbMATH DE Number: 7382628
zbMATH Keywords: bi-objective optimization
zbMATH Keywords: multiple criteria decision making
zbMATH Keywords: cardinality-constrained Markowitz portfolio investment problem
zbMATH Keywords: two-sided efficient frontier approximations
zbMATH Keywords: Chebyshev scalarization
author: Janusz Miroforidis
reviewed by: Yuliya S. Mishura
describes a project that uses: Genocop
MaRDI profile type: Publication
full work available at URL: s10898-021-01022-1
OpenAlex ID: W3159365730
cites work: A portfolio optimization model with three objectives and discrete variables
cites work: Heuristics for cardinality constrained portfolio optimization
cites work: A new method for mean-variance portfolio optimization with cardinality constraints
cites work: Q4451071
cites work: Applications of Multi-Objective Evolutionary Algorithms
cites work: Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems
cites work: Hybrid metaheuristics for constrained portfolio selection problems
cites work: Fast algorithms for sparse portfolio selection considering industries and investment styles
cites work: Multicriteria Optimization
cites work: Bound sets for biobjective combinatorial optimization problems
cites work: An MCDM approach to portfolio optimization.
cites work: Perspective cuts for a class of convex 0-1 mixed integer programs
cites work: Optimal cardinality constrained portfolio selection
cites work: Proper efficiency and the theory of vector maximization
cites work: Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints
cites work: Soft computing for complex multiple criteria decision making
cites work: Out of the mist -- towards decision-maker-friendly multiple criteria decision making support
cites work: Two-sided Pareto front approximations
cites work: On upper approximations of Pareto fronts
cites work: Cooperative multiobjective optimization with bounds on objective functions
cites work: Interactive multiple criteria decision making based on preference driven evolutionary multiobjective optimization with controllable accuracy
cites work: Multiple criteria decision making by multiobjective optimization. A toolbox
cites work: Selecting portfolios with fixed costs and minimum transaction lots
cites work: 60 years of portfolio optimization: practical challenges and current trends
cites work: Q4873721
cites work: Nonlinear multiobjective optimization
cites work: Enhancement of sandwich algorithms for approximating higher-dimensional convex Pareto sets
cites work: Approximation methods in multiobjective programming
cites work: Approximating the noninferior set in multiobjective linear programming problems
cites work: Encyclopedia of operations research and management science. Centennial edition.
cites work: An interactive weighted Tchebycheff procedure for multiple objective programming
cites work: Q4945548
cites work: Heuristic algorithms for the cardinality constrained efficient frontier
DOI: 10.1007/S10898-021-01022-1
description: scientific article; zbMATH DE number 7382628