On <i>g</i>>Evaluations with L<sup><i>p</i></sup> Domains under Jump Filtration

Abstract

Given p ∈ (1, 2), the unique Lp solutions of backward stochastic differential equations with jumps (BSDEJs) allow us to extend the notion of g−evaluations, in particular g−expectations, to the jump case with Lp domains. We explore many important properties of the extended g−evaluations including optional sampling, upcrossing inequality, Doob-Meyer decomposition, generator representation and Jensen’s inequality. Most of these results are important for the further development of jump-filtration consistent nonlinear expectations with Lp domains.