Dynamic Assessment Indices

TL;DR

This paper introduces a unified framework for dynamic monetary risk measures and acceptability indices using $L^0$-modules, providing theoretical generalizations and applications to stochastic processes.

Contribution

It develops a general theory of dynamic assessment indices and offers a robust representation, extending existing results with the use of $L^0$-modules.

Findings

Unified framework for dynamic risk measures and acceptability indices

Robust representation of conditional assessment indices

Application to stochastic processes

Abstract

This paper provides a unified framework, which allows, in particular, to study the structure of dynamic monetary risk measures and dynamic acceptability indices. The main mathematical tool, which we use here, and which allows us to significantly generalize existing results is the theory of $L^0$-modules. In the first part of the paper we develop the general theory and provide a robust representation of conditional assessment indices, and in the second part we apply this theory to dynamic acceptability indices acting on stochastic processes.