Minimal supersolutions of BSDEs with lower semicontinuous generators
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, p. 524-538

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.

DOI : https://doi.org/10.1214/12-AIHP523
Classification:  60H20,  60H30
Keywords: supersolutions of backward stochastic differential equations, semimartingale convergence
@article{AIHPB_2014__50_2_524_0,
     author = {Heyne, Gregor and Kupper, Michael and Mainberger, Christoph},
     title = {Minimal supersolutions of BSDEs with lower semicontinuous generators},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {2},
     year = {2014},
     pages = {524-538},
     doi = {10.1214/12-AIHP523},
     zbl = {1296.60173},
     mrnumber = {3189083},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2014__50_2_524_0}
}
Heyne, Gregor; Kupper, Michael; Mainberger, Christoph. Minimal supersolutions of BSDEs with lower semicontinuous generators. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, pp. 524-538. doi : 10.1214/12-AIHP523. http://www.numdam.org/item/AIHPB_2014__50_2_524_0/

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