Representation of weakly maxitive monetary risk measures and their rate functions

The present paper provides a representation result for monetary risk measures (i.e., monotone translation invariant functionals) satisfying weak maxitivity property. This can be understood as functional analytic generalization of Gärtner-Ellis large deviations theorem. In contrast to the classical theorem, rate function is computed on an arbitrary set continuous real-valued functions rather than dual space. As application main result, we establish deviation sequences sublinear expectations regular Hausdorff topological spaces.