Dynamic Coherent Acceptability Indices and their Applications to Finance

TL;DR

This paper develops a theoretical framework for dynamic coherent acceptability indices and risk measures in finance, establishing duality and representation theorems, and providing concrete examples and constructions.

Contribution

It introduces a novel duality and representation framework for dynamic coherent acceptability indices and risk measures in finance.

Findings

Established duality between dynamic coherent acceptability indices and risk measures

Derived a representation theorem using dynamically consistent probability measure sets

Constructed specific dynamic coherent acceptability indices, generalizing classical financial measures

Abstract

In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of so called dynamically consistent sequence of sets of probability measures. Based on these results, we give a specific construction of dynamic coherent acceptability indices. We also provide examples of dynamic coherent acceptability indices, both abstract and also some that generalize selected classical financial measures of portfolio performance.