Valuations and dynamic convex risk measures

TL;DR

This paper develops a framework for dynamic convex risk measures using valuation operators, emphasizing risk transfer and time consistency in finite settings, relevant for firms managing risk across subsidiaries.

Contribution

It introduces a new approach to dynamic convex risk measures based on valuation operators with simple axioms, highlighting risk transfer and time consistency.

Findings

Risk transfer properties are natural in the proposed framework.

Time consistency is established for the valuation operators.

Framework applies to finite time and sample spaces.

Abstract

This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a finite time set and finite sample space, we find natural risk-transfer and time-consistency properties for a firm seeking to spread its risk across a group of subsidiaries.