Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Dual representation of minimal supersolutions of convex BSDEs

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

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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.


Nous donnons une représentation duale des sur-solutions minimales d’équations différentielles stochastiques rétrogrades avec des conditions terminales intégrables mais non nécessairement bornées, et de faibles hypotheses sur le générateur qui peut de plus dépendre de la valeur processus de l’équation même. Réciproquement, nous montrons que toute mesure de risque dynamique satisfaisant une telle représentation duale provient d’une EDSR. Nous donnons aussi une condition sous laquelle une sur-solution d’EDSR est en fait une solution.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 52, Number 2 (2016), 868-887.

Received: 12 August 2013
Revised: 27 June 2014
Accepted: 10 December 2014
First available in Project Euclid: 4 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H20: Stochastic integral equations 60H30: Applications of stochastic analysis (to PDE, etc.)

Convex duality Supersolutions of BSDEs Cash-subadditive risk measures


Drapeau, Samuel; Kupper, Michael; Rosazza Gianin, Emanuela; Tangpi, Ludovic. Dual representation of minimal supersolutions of convex BSDEs. Ann. Inst. H. Poincaré Probab. Statist. 52 (2016), no. 2, 868--887. doi:10.1214/14-AIHP664.

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