
Second order BSDEs with jumps: existence and probabilistic representation for fully-nonlinear PIDEs
Kazi-Tani, Mohamed Nabil; Possamaï, Dylan; Zhou, Chao (2015), Second order BSDEs with jumps: existence and probabilistic representation for fully-nonlinear PIDEs, Electronic Journal of Probability, 20, 65. 10.1214/EJP.v20-3569
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Article accepté pour publication ou publiéDate
2015Journal name
Electronic Journal of ProbabilityVolume
20Number
65Publisher
Electronic Journal of Probability and Electronic Communications in Probability
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Show full item recordAbstract (EN)
In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in an accompanying paper. We prove existence of these equations by a direct method, thus providing complete wellposedness for 2BSDEJs. These equations are a natural candidate for the probabilistic interpretation of some fully non-linear partial integro-differential equations, which is the point of the second part of this work. We prove a non-linear Feynman-Kac formula and show that solutions to 2BSDEJs provide viscosity solutions of the associated PIDEs.Subjects / Keywords
Second order backward stochastic differential equation; backward stochastic differential equation with jumps; model uncertainty; PIDEs; viscosity solutions.Related items
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