# Worst portfolios for dynamic monetary utility processes

## TL;DR

This paper investigates the worst-case portfolios for certain dynamic monetary utility functions, introducing a new concept of comonotonicity and establishing conditions for worst-case scenarios over time.

## Contribution

It introduces a novel concept of comonotonicity for stochastic processes and links worst portfolios across different time periods for dynamic utility functions.

## Key findings

- Existence of worst portfolios proven using comonotonicity.
- Relations between worst portfolios at different times established.
- Conditions for maximum in utility representations identified.

## Abstract

We study the worst portfolios for a class of law invariant dynamic monetary utility functions with domain in a class of stochastic processes. The concept of comonotonicity is introduced for these processes in order to prove the existence of worst portfolios. Using robust representations of monetary utility function processes in discrete time, a relation between the worst portfolios at different periods of time is presented. Finally, we study conditions to achieve the maximum in the representation theorems for concave monetary utility functions that are continuous for bounded decreasing sequences.