An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior

TL;DR

This paper investigates the long-term behavior of forward entropic risk measures using ergodic BSDEs, showing exponential convergence to a constant and comparing with classical measures.

Contribution

It provides a novel representation of forward entropic risk measures and analyzes their asymptotic behavior for long maturities using ergodic BSDE techniques.

Findings

Forward entropic risk measures converge exponentially fast to a constant.

A parity relation between forward entropic and classical risk measures is established.

The paper offers duality-based representations of the risk measures.

Abstract

Using elements from the theory of ergodic backward stochastic differential equations (BSDE), we study the behavior of forward entropic risk measures. We provide their general representation results (via both BSDE and convex duality) and examine their behavior for risk positions of long maturities. We show that forward entropic risk measures converge to some constant exponentially fast. We also compare them with their classical counterparts and derive a parity result.