We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on Lp spaces, while the other approach utilizes module-based convex analysis where conditional risk measures are defined...

This paper provides sufficient and necessary conditions for the existence of equilibrium pricing rules for monetary utility functions under convex consumption constraints. These utility functions are characterized by the assumption of a fully fungible numeraire asset ("cash"). Each agent's...