Applied Mathematics & Optimization

, Volume 79, Issue 1, pp 87–129 | Cite as

Jump-Filtration Consistent Nonlinear Expectations with \({\mathbb {L}^{p}}\) Domains

  • Jing Liu
  • Song YaoEmail author


Given \(p \in (1,2]\), the wellposedness of backward stochastic differential equations with jumps (BSDEJs) in \(\mathbb {L}^p\) sense gives rise to a so-called g-expectation with \(\mathbb {L}^p\) domain under the jump filtration (the one generated by a Brownian motion and a Poisson random measure). In this paper, we extend such a g-expectation to a nonlinear expectation \(\mathcal{E}\) with \(\mathbb {L}^p\) domain that is consistent with the jump filtration. We study the basic (martingale) properties of the jump-filtration consistent nonlinear expectation \(\mathcal{E}\) and show that under certain domination condition, the nonlinear expectation \(\mathcal{E}\) can be represented by some g-expectation.


Backward stochastic differential equations with jumps \(\mathbb {L}^p\) solutions g-Expectations Nonlinear expectations consistent with jump filtration Optional sampling Doob–Meyer decomposition Representation theorem 

Mathematics Subject Classification

60H10 91B30 60F25 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA

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