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

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.