Dynamic Limit Growth Indices in Discrete Time

TL;DR

This paper introduces Dynamic Limit Growth Indices, a new class of measures for assessing long-term portfolio performance in discrete time, connecting them with existing risk measures and establishing their properties and time consistency.

Contribution

It defines Dynamic Limit Growth Indices, explores their properties, links them with classical indices, and proposes a new concept of time consistency for these measures.

Findings

Established necessary and sufficient conditions for these indices to be dynamic assessment indices.

Connected Dynamic Limit Growth Indices with classical dynamic acceptability indices.

Proposed a new definition of time consistency and analyzed it for key examples.

Abstract

We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of measures, and in particular, we provide necessary and sufficient condition for a Dynamic Limit Growth Index to be a dynamic assessment index. We also establish their connection with classical dynamic acceptability indices, and we show how to construct examples of Dynamic Limit Growth Indices using dynamic risk measures and dynamic certainty equivalents. Finally, we propose a new definition of time consistency, suitable for these indices, and we study time consistency for the most notable representative of this class -- the dynamic analog of risk sensitive criterion.