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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Jing Liu & Song Yao

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  1. Jing Liu
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  2. Song Yao
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Correspondence to Song Yao.

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Liu, J., Yao, S. Jump-Filtration Consistent Nonlinear Expectations with \({\mathbb {L}^{p}}\) Domains. Appl Math Optim 79, 87–129 (2019). https://doi.org/10.1007/s00245-017-9422-4

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