Decision making under risk with continuous states of nature

Many real-world decision making situation are associated with uncertainty regarding future state of the World. Traditionally, in such situation different (and discrete) scenarios – future states of nature – are considered. This domain of decision making is denoted as decision making under risk. However, limitation to some set of discrete scenarios is somewhat unnatural as future reality might not choose one of considered scenarios, but some other scenario or a scenario in between. The aim of this paper is to propose a more natural approach with continuum states of nature, where all scenarios expressed by their probability density function from some reasonable interval are taken into consideration. The approach is illustrated by a numerical example and is compared with the corresponding decision making under risk with discrete states of nature.