Just Previsions
This provides a structural decomposition for a broad class of functionals in mathematical finance and decision theory, but the results are theoretical and incremental relative to existing work on sub/superlinear previsions.
The paper characterizes all previsions (positively homogeneous functionals) as infima of sublinear previsions and suprema of superlinear previsions under mild conditions, establishing homeomorphisms between spaces of previsions and hyperspaces of sublinear/superlinear previsions.
Previsions are positively homogeneous functionals, and are generalized forms of integration functionals. We investigate previsions -- just previsions, not sublinear or superlinear previsions as in previous work. We show that every prevision can be expressed as an infimum of sublinear previsions, and as a supremum of superlinear previsions under mild conditions. This extends to homeomorphisms between spaces of previsions and certain hyperspaces over spaces of sublinear or superlinear previsions, which can also be characterized in terms of orthogonality relations, making the construction a variant of a double powerspace construction.