PGP for portfolio optimization: application to ESG index family

Ilyes Abid*, Christian Urom, Jonathan Peillex, Majdi Karmani, Gideon Ndubuisi

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
20 Downloads (Pure)


The conventional portfolio design approach assumes Gaussian return distributions, but this is not accurate in practice. Asymmetric and heavy-tailed return distributions necessitate consideration of higher-order moments such as skewness and kurtosis, in addition to mean and variance. This study proposes a multi-objective approach using a mean-variance-skewness-kurtosis model to construct a diversified portfolio. A parametrized polynomial goal programming (PGP) method is used to optimize the portfolio by maximizing returns and skewness while minimizing variance and kurtosis. Empirical data from the S &P ESG index family is used, and PGP generates multiple portfolios reflecting investors’ preferences for the four moments. To compare between the obtained portfolios, we represent the empirical cumulative distribution of the portfolio returns for all studied values of weights and show how this can be used to assist the inverstor in selecting the best set of weights.
Original languageEnglish
Number of pages13
JournalAnnals of Operations Research
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • High-order portfolios
  • Kurtosis
  • PGP method
  • Skewness


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