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.
Drapeau, S., Kupper, M., ROSAZZA GIANIN, E., Tangpi, L. (2016). Dual representation of minimal supersolutions of convex BSDEs. ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 52(2), 868-887 [10.1214/14-AIHP664].
Dual representation of minimal supersolutions of convex BSDEs
ROSAZZA GIANIN, EMANUELAPenultimo
;
2016
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.
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