Geodesic
A solution guaranteed for a risk-neutral person to a one-criterion problem: an analog of the vector saddle point
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 52 (2018), pp. 13-32

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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.
Keywords: strategy, uncertainty, criterion, Slater optimum, vector saddle point.
Mots-clés : Pareto optimum 
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     author = {V. I. Zhukovskii and M. V. Boldyrev and M. M. Kirichenko},
     title = {A solution guaranteed for a risk-neutral person to a one-criterion problem: an analog of the vector saddle point},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {13--32},
     publisher = {mathdoc},
     volume = {52},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2018_52_a1/}
}
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V. I. Zhukovskii; M. V. Boldyrev; M. M. Kirichenko. A solution guaranteed for a risk-neutral person to a one-criterion problem: an analog of the vector saddle point. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 52 (2018), pp. 13-32. http://geodesic.mathdoc.fr/item/IIMI_2018_52_a1/