# Commonotonicity and time consistency for Lebesgue continuous monetary utility functions

## TL;DR

This paper proves that monetary utility functions cannot be both commonotonic and time consistent, providing insights into their incompatibility and exploring related properties on atomless probability spaces.

## Contribution

It establishes the fundamental incompatibility between commonotonicity and time consistency for monetary utility functions, with additional results on atomless probability spaces.

## Key findings

- Commonotonicity and time consistency cannot coexist in monetary utility functions.
- Additional results are provided for atomless and conditionally atomless probability spaces.
- The paper clarifies the structural limitations of utility functions in financial modeling.

## Abstract

It is proved that commonotonicity and time consistence for monetary utility functions do not go together. I also gives additional results on atomless and conditionally atomless probability spaces.