Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Minimal supersolutions of BSDEs with lower semicontinuous generators

Gregor Heyne, Michael Kupper, and Christoph Mainberger

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We study minimal supersolutions of backward stochastic differential equations. We show the existence and uniqueness of the minimal supersolution, if the generator is jointly lower semicontinuous, bounded from below by an affine function of the control variable, and satisfies a specific normalization property. Semimartingale convergence is used to establish the main result.


Nous étudions des sur-solutions minimales d’équations stochastiques rétrogrades. Nous montrons l’existence et l’unicité de telles sur-solutions minimales lorsque le générateur est conjointement semi-continu inférieurement, minoré par une fonction affine de la variable de contrôle et satisfait une condition spécifique de normalisation. Le résultat principal est obtenu en utilisant une convergence de semi-martingales.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 50, Number 2 (2014), 524-538.

First available in Project Euclid: 26 March 2014

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

Supersolutions of backward stochastic differential equations Semimartingale convergence


Heyne, Gregor; Kupper, Michael; Mainberger, Christoph. Minimal supersolutions of BSDEs with lower semicontinuous generators. Ann. Inst. H. Poincaré Probab. Statist. 50 (2014), no. 2, 524--538. doi:10.1214/12-AIHP523.

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