Modeling portfolio efficiency using stochastic optimization with incomplete information and partial uncertainty

• Published in: Annals of operations research Vol. 334; no. 1-3; pp. 241 - 263
• Main Authors: La Torre, D., Mendivil, F., Rocca, M.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2024; Springer; Springer Nature B.V
• Subjects: Asset allocation; Business and Management; Combinatorics; Efficiency; Fuzzy sets; Mathematical optimization; Operations research; Operations Research/Decision Theory; Optimization; Optimization techniques; Original Research; Portfolio management; Probability; Probability distribution; Probability theory; Random variables; Set theory; Stochastic processes; Theory of Computation; Uncertainty; Utility functions; France; Portfolio optimization; Stochastic dominance; Set-valued analysis; Portfolio efficiency; Incomplete information; Partial uncertainty
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-021-04372-x

Efficiency plays a crucial role in portfolio optimization. This notion is formulated by means of stochastic optimization techniques. Very often this problem is subject to partial uncertainty or incomplete information on the probability distribution and on the preferences expressed by means of the utility function. In this case both the objective function and the underlying probability measure are not known with precision. To address this kind of issues, we propose to model the notion of incomplete information by means of set-valued analysis and, therefore, we propose two different extensions of the classical model. In the first one we rely on the notion of set-valued function while the second one utilizes the notion of set-valued probability. For both of them we investigate stability properties. These results are also linked to the notion of robustness of the aforementioned problem. Finally we apply the obtained results to portfolio theory and stochastic dominance.