Electronic Journal of Probability

Second order BSDEs with jumps: existence and probabilistic representation for fully-nonlinear PIDEs

Nabil Kazi-Tani, Dylan Possamaï, and Chao Zhou

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

Second order backward stochastic differential equation backward stochastic differential equation with jumps model uncertainty PIDEs viscosity solutions

This work is licensed under aCreative Commons Attribution 3.0 License.


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

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