Behavioral portfolio optimization via cumulative prospect theory with a symmetric alternating direction method of multipliers

Amidst prevailing uncertainties in investment landscapes and heterogeneous investor risk attitudes toward gains and losses, this study investigates behavioral portfolio selection under a flexible investment horizon. We employ cumulative prospect theory (CPT) to model preferences, integrating mean-variance criteria with asymmetric risk behaviors. By extending the mean-variance framework, our model balances exploiting existing opportunities and exploring new assets to derive adaptive strategies. The optimization problem is solved using the symmetric alternating direction method of multipliers and the pooling-adjacent-violators algorithm, chosen for their efficacy in handling non-convexity and ordinal constraints. The optimal number of new assets to explore is determined via an integer programming problem, solved with a modified particle swarm optimization algorithm. In addition, we incorporate environmental, social, and governance (ESG) metrics to evaluate their impact on sustainable behavioral portfolios. Empirical analyses using real-world equity datasets demonstrate that strategic exploration enhances returns, reduces portfolio risk, and improves investment efficiency. The effectiveness of the proposed algorithm is also illustrated. The results highlight the value of adaptive horizon planning, ESG integration, and CPT preferences in portfolio optimization, offering actionable insights for investors navigating dynamic markets.