On one definition of uncertainty

Article type: Research Article

Authors: Ivanenko, Yaroslav^; | Pasichnichenko, Illia

Affiliations: Institute of Applied System Analysis, Prospect Peremohy, 37, Kyiv, 03056, Ukraine. E-mails: {yarsky1, io.pasich}@gmail.com

Note: [] Corresponding author. E-mail: yarsky1@gmail.com

Abstract: In this paper uncertainty is defined as non-uniqueness of projection of a preference on consequences onto the set of preferences on acts in a choice problem. Such definition of uncertainty seems natural, but it is not very well known despite being compatible with M. Allais principle of internal coherence [Econometrica 21(4) (1953), 503–546]. It is shown that absence of arbitrage opportunity, in the sense of the Arrow–Debreu model of securities market with a risk-less asset, represents an example and a particular case of existence of uncertainty, defined in the above sense.

Keywords: Binary relations, uncertainty, ambiguity, arbitrage opportunity

DOI: 10.3233/RDA-140106

Journal: Risk and Decision Analysis, vol. 5, no. 2-3, pp. 139-148, 2014