Representation of filtration-consistent nonlinear expectation by g-expectation in general framework

Abstract

In this paper, we mainly study nonlinear expectations on the general domain whose elements can be measurable with respect to ${\mathcal{F}}_{\infty },$ a σ-filed generated by the whole path of Brownian motion on infinite time interval. And we obtain that every translation invariant filtration consistent nonlinear expectation with some dominated condition can be represented by a g-expectation introduced by a backward stochastic differential equation on the general time horizon.

Keywords:

• BSDE
• infinite horizon
• nonlinear expectation
• g-expectation

2000 MSC:

• 60H99 60H30

Additional information

Funding

Research supported by the National Natural Science Foundation of China (Nos. 11626146, 71502071, 11371362), the China Postdoctoral Science Foundation (No. 2019M652420), and the Shandong Provincial Natural Science Foundation (Nos. ZR2016AP05, ZR2015PG001).