<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The article is devoted to the development and study of a model of a minimal risk portfolio under conditions of hybrid uncertainty of possibilistic-probabilistic type. In this model, the interaction of fuzzy parameters is described by both the strongest and the weakest triangular norms. The formula for variance of a portfolio is given that allows for estimating its risk. Models of acceptable portfolios are based on the principle of expected possibility or on the basis of fulfilling the restriction on the possibility/necessity and probability of the level of portfolio return that is acceptable to an investor. Equivalent deterministic analogues of the models are constructed and their solution methods are developed. Theorems describing a set of investment opportunities are proven. The obtained results are demonstrated on a model example.</p>
</abstract>

The article is devoted to the development and study of a model of a minimal risk portfolio under conditions of hybrid uncertainty of possibilistic-probabilistic type. In this model, the interaction of fuzzy parameters is described by both the strongest and the weakest triangular norms. The formula for variance of a portfolio is given that allows for estimating its risk. Models of acceptable portfolios are based on the principle of expected possibility or on the basis of fulfilling the restriction on the possibility/necessity and probability of the level of portfolio return that is acceptable to an investor. Equivalent deterministic analogues of the models are constructed and their solution methods are developed. Theorems describing a set of investment opportunities are proven. The obtained results are demonstrated on a model example.

Model of a minimal risk portfolio under hybrid uncertainty

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Model of a minimal risk portfolio under hybrid uncertainty"}

The article is devoted to the development and study of a model of a minimal risk portfolio under conditions of hybrid uncertainty of...

Model of a minimal risk portfolio under hybrid uncertainty

Published Online: Jun 28, 2022

Page range: 315 - 333

Received: Sep 01, 2020

Accepted: Feb 01, 2021

DOI: https://doi.org/10.2478/candc-2021-0016

Keywords
minimum risk portfolio, hybrid uncertainty, possibility, necessity, strongest -norm, weakest -norm, fuzzy random variable

© 2021 Alexander V. Yazenin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Model of a minimal risk portfolio under hybrid uncertainty

Published Online: Jun 28, 2022

Page range: 315 - 333

Received: Sep 01, 2020

Accepted: Feb 01, 2021

DOI: https://doi.org/10.2478/candc-2021-0016

Keywordsminimum risk portfolio, hybrid uncertainty, possibility, necessity, strongest -norm, weakest -norm, fuzzy random variable

© 2021 Alexander V. Yazenin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
minimum risk portfolio, hybrid uncertainty, possibility, necessity, strongest -norm, weakest -norm, fuzzy random variable