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

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 anal...

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Bibliographic Details
Published in:International transactions in operational research Vol. 26; no. 2; pp. 389 - 414
Main Authors: Mencarelli, Luca, D'Ambrosio, Claudia
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.03.2019
Wiley
Subjects:
Computer Science
Constraint modelling
convex MINLP
Convexity
Empirical analysis
exact methods
mixed‐integer quadratic programming
Operations Research
Portfolio management
portfolio selection
Probabilistic models
Quadratic programming
robust and probabilistic optimization
Variance analysis
ISSN:0969-6016, 1475-3995
Online Access:Get full text
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Summary: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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ISSN:0969-6016
1475-3995
DOI:10.1111/itor.12541