Dual Representation of Minimal Supersolutions of Convex BSDEs

TL;DR

This paper establishes a dual representation for minimal supersolutions of convex BSDEs with integrable terminal conditions, linking them to dynamic risk measures and providing conditions for supersolutions to be actual solutions.

Contribution

It introduces a dual representation framework for convex BSDE supersolutions with integrable terminal conditions and connects these to dynamic risk measures.

Findings

Dual representation of minimal supersolutions established

Connection between supersolutions and dynamic risk measures demonstrated

Conditions identified under which supersolutions are solutions

Abstract

We give a dual representation of minimal supersolutions of BSDEs with non-bounded, but integrable terminal conditions and under weak requirements on the generator which is allowed to depend on the value process of the equation. Conversely, we show that any dynamic risk measure satisfying such a dual representation stems from a BSDE. We also give a condition under which a supersolution of a BSDE is even a solution.