Bi-Objective Portfolio Optimization Under ESG Volatility via a MOPSO-Deep Learning Algorithm

Imma Lory Aprea, Gianni Bosi (), Gabriele Sbaiz and Salvatore Scognamiglio
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Imma Lory Aprea: Department of Economics, Law, Cybersecurity, and Sports Sciences, University of Naples “Parthenope”, Guglielmo Pepe Street, 80035 Nola, Italy
Gianni Bosi: Department of Economics, Business, Mathematics and Statistics, University of Trieste, A. Valerio Street, 4/1, 34127 Trieste, Italy
Gabriele Sbaiz: Department of Economics, Business, Mathematics and Statistics, University of Trieste, A. Valerio Street, 4/1, 34127 Trieste, Italy
Salvatore Scognamiglio: Department of Management and Quantitative Studies, University of Naples “Parthenope”, Generale Parisi Street, 13, 80132 Naples, Italy

Mathematics, 2025, vol. 13, issue 20, 1-31

Abstract: In this paper, we tackle a bi-objective optimization problem in which we aim to maximize the portfolio diversification and, at the same time, minimize the portfolio volatility, where the ESG (Environmental, Social, and Governance) information is incorporated. More specifically, we extend the standard portfolio volatility framework based on the financial aspects to a new paradigm where the sustainable credits are taken into account. In the portfolio’s construction, we consider the classical constraints concerning budget and box requirements. To deal with these new asset allocation models, in this paper, we develop an improved Multi-Objective Particle Swarm Optimizer (MOPSO) embedded with ad hoc repair and projection operators to satisfy the constraints. Moreover, we implement a deep learning architecture to improve the quality of estimating the portfolio diversification objective. Finally, we conduct empirical tests on datasets from three different countries’ markets to illustrate the effectiveness of the proposed strategies, accounting for various levels of ESG volatility.

Keywords: sustainable bi-objective portfolio optimization; ESG volatility; MOPSO; deep learning architecture (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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