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.

Modeling portfolio efficiency using stochastic optimization with incomplete information and partial uncertainty / D. La Torre, F. Mendivil, M. Rocca. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - (2021), pp. 1-23. [Epub ahead of print] [10.1007/s10479-021-04372-x]

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

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC)
Incomplete information; Partial uncertainty; Portfolio efficiency; Portfolio optimization; Set-valued analysis; Stochastic dominance
Settore MAT/09 - Ricerca Operativa
2021
10-nov-2021
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/963717`
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