Jensen’s inequality for \(g\)-expectations in general filtration spaces. (English) Zbl 1455.60072
Summary: In this paper, we investigate the properties of BSDEs in general filtration spaces based on the transposition solutions. We obtain a result that Jensen’s inequality holds under the \(g\)-expectation and conditional \(g\)-expectation in general filtration spaces if and only if \(g\) is independent of \(y\) and super-homogeneous in \(z\).
MSC:
| 60G65 | Nonlinear processes (e.g., \(G\)-Brownian motion, \(G\)-Lévy processes) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
Jensen’s inequality; \(g\)-expectation; filtration; backward stochastic differential equationReferences:
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