A representation for filtration-consistent nonlinear expectations and its application

Abstract

In this paper, we consider filtration-consistent nonlinear expectations which satisfy a general domination condition. We show that filtration-consistent nonlinear expectations can be represented by g-expectations defined by the solutions of backward stochastic differential equations, whose generators are independent of y and uniformly continuous in z. As an application, we establish a concentration inequality for time-consistent risk measures.

Keywords:

• Backward stochastic differential equation
• Doob-Meyer decomposition
• Filtration-consisitent expectation
• g-expectation
• Time-consistent risk measure

AMS SUBJECT CLASSIFICATION:

• 60H10

Additional information

Funding

The authors would like to thank the anonymous referee for valuable comments and suggestions. The authors are supported by the National Natural Science Foundation of China (No. 11571024) and the Humanities and Social Science Foundation of Ministry of Education of China (No. 20YJCZH245).