Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 65, 31 pp.
Second order BSDEs with jumps: existence and probabilistic representation for fully-nonlinear PIDEs
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.
Electron. J. Probab., Volume 20 (2015), paper no. 65, 31 pp.
Accepted: 14 June 2015
First available in Project Euclid: 4 June 2016
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Kazi-Tani, Nabil; Possamaï, Dylan; Zhou, Chao. Second order BSDEs with jumps: existence and probabilistic representation for fully-nonlinear PIDEs. Electron. J. Probab. 20 (2015), paper no. 65, 31 pp. doi:10.1214/EJP.v20-3569. https://projecteuclid.org/euclid.ejp/1465067171