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2018 Supermartingale decomposition theorem under $G$-expectation
Hanwu Li, Shige Peng, Yongsheng Song
Electron. J. Probab. 23: 1-20 (2018). DOI: 10.1214/18-EJP173

Abstract

The objective of this paper is to establish the decomposition theorem for supermartingales under the $G$-framework. We first introduce a $g$-nonlinear expectation via a kind of $G$-BSDE and the associated supermartingales. We have shown that this kind of supermartingales has the decomposition similar to the classical case. The main ideas are to apply the property on uniform continuity of $S_G^\beta (0,T)$, the representation of the solution to $G$-BSDE and the approximation method via penalization.

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Hanwu Li. Shige Peng. Yongsheng Song. "Supermartingale decomposition theorem under $G$-expectation." Electron. J. Probab. 23 1 - 20, 2018. https://doi.org/10.1214/18-EJP173

Information

Received: 8 March 2017; Accepted: 28 April 2018; Published: 2018
First available in Project Euclid: 1 June 2018

zbMATH: 06924662
MathSciNet: MR3814244
Digital Object Identifier: 10.1214/18-EJP173

Subjects:
Primary: 60H10, 60H30

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