Maturity-independent risk measures

TL;DR

This paper introduces the concept of maturity-independent risk measures, contrasting them with traditional measures, and demonstrates their construction and applicability in various financial models, highlighting limitations of existing measures.

Contribution

It presents a novel class of maturity-independent risk measures and provides concrete examples in both discrete and continuous financial models.

Findings

Some widely used risk measures cannot be adapted to maturity-independent versions

A large class of maturity-independent risk measures is constructed

Examples are provided in both finite probability and diffusion frameworks

Abstract

The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion framework, that, surprisingly, some of the widely utilized risk measures cannot be used to build maturity-independent counterparts. We construct a large class of maturity-independent risk measures and give representative examples in both continuous- and discrete-time financial models.