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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Abstract

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

Source
Electron. J. Probab., Volume 20 (2015), paper no. 65, 31 pp.

Dates
Accepted: 14 June 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067171

Digital Object Identifier
doi:10.1214/EJP.v20-3569

Mathematical Reviews number (MathSciNet)
MR3361253

Zentralblatt MATH identifier
1321.60125

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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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