A neural network-particle swarm solver for sustainable portfolio optimization problems

In this paper, the main goal is to tackle a sustainable portfolio optimization problem in which we aim to minimize a tail-dependence risk measure. More specifically, the considered risk measure is represented by the Delta Conditional Value-at-Risk, a tail-dependence measure meant to quantify the potential losses of a portfolio due to the riskiness associated with an individual asset or a group of assets. In addition, in the portfolio construction, we take into account some real-world trading constraints. On the one hand, we impose stock market restrictions through buy-in thresholds and budget constraints. Moreover, a minimum level of guaranteed expected return is required. On the other hand, a turnover threshold restricts the total amount of trades allowed in the rebalancing phases. Finally, in order to meet the growing appetite for sustainable investment, we introduce a green threshold into the portfolio's design. To deal with these asset allocation models, in this paper we develop an improved hybrid Particle Swarm Optimizer (PSO) that is dynamically adjusted by a neural network architecture embedded with a suitable constraint-handling procedure. The neural network paradigm is fundamental for enhancing the basic PSO's performance and improving the quality of estimating the Delta Conditional Value-at-Risk. Finally, we conduct empirical tests on two different American datasets to illustrate the effectiveness of the proposed strategies and evaluate the performance of our investments as the sustainable preferences vary.