Behavioral dynamic portfolio selection with S-shaped utility and epsilon-contaminations

• Published in: European journal of operational research Vol. 325; no. 3; pp. 500 - 515
• Main Authors: Cinfrignini, Andrea, Petturiti, Davide, Vantaggi, Barbara
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.09.2025
• Subjects: Behavioral investor; Epsilon-contamination; Portfolio optimization; S-shaped utility function; Uncertainty modeling; Portfolio optimization; S-shaped utility function; Uncertainty modeling; Epsilon-contamination; Behavioral investor
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2025.03.029

Inspired by the classical cumulative prospect theory (CPT), we propose a CPT-like functional characterized by the modeling of uncertainty on gains and losses through two epsilon-contaminations of a reference probability measure. Such functional is used to perform a dynamic portfolio selection in a finite horizon binomial market model, reducing it to an iterative search problem over the set of optimal solutions of a family of pairs of non-linear optimization problems on the final wealth. Despite the computational hardness of the resulting pairs of problems, epsilon-contaminations allow to represent each solution in terms of the partition generated by the stock price random variable at maturity, obtaining a sensible reduction of variables and constraints. In turn, the optimization task can be reduced to the maximization of a real-valued function of one real variable, revealing the possible ill-posedness of the problem. The resulting model is discussed by means of some paradigmatic examples on market data and a sensitivity analysis. •Modeling ambiguity on gains and losses via epsilon-contaminations.•Optimal dynamic portfolio selection as maximization of a CPT-like functional.•Hardness and ill-posedness of the problem and variable-constraint reduction.•Examples of agent behaviors and sensitivity analysis of ambiguity thresholds.