Jump-Filtration Consistent Nonlinear Expectations with Lp Domains

Abstract

Given p ∈ (1,2), the wellposedness of backward stochastic differential equations with jumps (BSDEJs) in Lp sense gives rise to a general (conditional) nonlinear expectation with Lp domain that is consistent with the filtration generated by a Brownian motion and a Poisson random measure (jump filtration). Under certain domination condition, such a nonlinear expectation preserves many basic (martingale) properties of the classic linear expectations and thus can be represented by the Lp solutions of BSDEJs with a deterministic generator that is independent of y and Lipschitz in (z,u).