A solution guaranteed for a risk-neutral person to a one-criterion problem: an analog of the vector saddle point

V. I. Zhukovskii ; M. V. Boldyrev ; M. M. Kirichenko

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 52 (2018), pp. 13-32.

Résumé

What can be people's attitude towards risk? In a series of financial economics publications, three main attitudes towards risk are distinguished: risk-averse; risk-neutral; risk-loving. It is inherent for risk-averse decision makers to follow the principle of guaranteed results (maximin). Risk-loving decision makers are prone to following the principle of Niehans–Savage's principle of minimax regret. This article defines the concept of a solution, weakly guaranteed simultaneously for outcomes and risks, to a one-criterion problem with uncertainty (OCPU) (the formalization is based on the concept of a vector saddle point from the theory of multicriteria problems with uncertainty) for risk-neutral decision makers. Sufficient conditions are established with the help of which an explicit form of the introduced solution for a sufficiently general form of OCPU with a limited uncertainty is found.

Détail

Keywords: strategy, uncertainty, criterion, Slater optimum, vector saddle point.
Mots-clés : Pareto optimum

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