Intrinsic risk measures

TL;DR

This paper introduces intrinsic risk measures as a new way to assess financial risk, focusing on internal resources and minimal adjustments needed to reach acceptability, offering advantages over traditional external capital-based measures.

Contribution

It proposes intrinsic risk measures that use only internal resources, providing a direct and flexible approach to risk assessment that preserves key properties and extends existing monetary risk measures.

Findings

Intrinsic risk measures avoid infinite values.

They allow a free choice of eligible assets.

A dual representation on convex acceptance sets is derived.

Abstract

Monetary risk measures are usually interpreted as the smallest amount of external capital that must be added to a financial position to make it acceptable. We propose a new concept: intrinsic risk measures and argue that this approach provides a direct path from unacceptable positions towards the acceptance set. Intrinsic risk measures use only internal resources and return the smallest percentage of the currently held financial position which has to be sold and reinvested into an eligible asset such that the resulting position becomes acceptable. While avoiding the problem of infinite values, intrinsic risk measures allow a free choice of the eligible asset and they preserve desired properties such as monotonicity and quasi-convexity. A dual representation on convex acceptance sets is derived and the link of intrinsic risk measures to their monetary counterparts on cones is detailed.