Strictly Positive Functionals in Orlicz Spaces

In this short paper, we do prove how to define strictly positive functionals in dual pairs of Orlicz Spaces. These Orlicz Spaces are endowed with the pointwise partial ordering. The Young functions that imply the definition of these dual pairs is significant for the difference between them. These strictly positive functionals imply that the No -Arbitrage pricing functionals in Incomplete Markets are well -defined. Orlicz Spaces are considered in Mathematical Finance, since the form of the Utility Functions for the individuals /investors is an Expected Utility Function.