Dual Representation of Minimal Supersolutions of Convex BSDEs

Samuel Drapeau, Michael Kupper, Emanuela Rosazza Gianin, Ludovic Tangpi

Published 2013-08-06, updated 2014-06-27Version 2

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.