Guaranteed risks and outcomes in “game against nature”

One-criteria problem under uncertainty is considered. There are only the limits of change that are known about uncertainty. The two concepts of formalization of guaranteed (for outcomes and risks simultaneously) solution are offered. The first concept is based on the method of decision-making in two-level hierarchical game. The second concept is based on the vector-maximin definition. The explicit form of solution under linear-quadratic criterion is found.