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Reflected backward stochastic differential equations with jumps and partial integro-differential variational inequalities

Sulem, Agnès; Quenez, Marie-Claire; Dumitrescu, Roxana (2013), Reflected backward stochastic differential equations with jumps and partial integro-differential variational inequalities, p. 23. https://basepub.dauphine.fr/handle/123456789/10925

Type
Rapport
External document link
http://hal.inria.fr/hal-00780601
Date
2013
Pages
23
Metadata
Show full item record
Author(s)
Sulem, Agnès
Quenez, Marie-Claire
Dumitrescu, Roxana
Abstract (FR)
On étudie le lien entre les équations différentielles stochastiques rétrogrades réfléchies avec sauts (EDSR réfléchies) et les inéquations variationnelles integro-différentielles (IVID). Dans un cadre markovien, on montre que la solution de l'EDSR réfléchie avec sauts correspond à l'unique solution de viscosité de l'IVID. On applique ces résultats à l'étude d'un problème d'arrêt optimal pour les mesures de risque dynamiques induites par des EDSR avec sauts.
Abstract (EN)
We study the links between reflected backward stochastic differential equations (reflected BSDEs) with jumps and partial integro-differential variational inequalities (PIDVIs). In a Markovian framework, we show that the solution of the reflected BSDE corresponds to the unique viscosity solution of the PIDVI. We apply these results to an optimal stopping problem for dynamic risk measures induced by BSDEs with jumps.
Subjects / Keywords
dynamic risk-measures; optimal stopping; partial integro-differential variational inequality; viscosity solution; Reflected backward stochastic differential equations with jumps

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