Convex Increasing Functionals on $C_b(X)$ Spaces

TL;DR

This paper demonstrates that convex functions on bounded continuous functions spaces, under mild conditions, can be represented via sigma additive measures, extending previous mathematical results.

Contribution

It generalizes existing theorems by showing convex functionals on $C_b(X)$ spaces can be represented with sigma additive measures under weaker assumptions.

Findings

Convex functions on $C_b(X)$ can be represented using sigma additive measures.

The result extends prior work by Cheridito, Kupper, and Tangpi.

The representation holds under mild continuity conditions.

Abstract

We prove that convex functions on a $C_b(X)$ space satisfying a mild continuity condition can be represented using sigma additive measures. This generalises a result of Cheridito, Kupper and Tangpi,