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Complex portfolio selection via convex mixed‐integer quadratic programming: a survey
Author(s) -
Mencarelli Luca,
D'Ambrosio Claudia
Publication year - 2019
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12541
Subject(s) - selection (genetic algorithm) , mathematical optimization , portfolio , probabilistic logic , quadratic programming , convexity , portfolio optimization , computer science , integer programming , quadratic equation , convex optimization , modern portfolio theory , variance (accounting) , integer (computer science) , mathematics , regular polygon , artificial intelligence , economics , finance , geometry , accounting , programming language
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.