Electronic Journal of Probability
- Electron. J. Probab.
- Volume 23 (2018), paper no. 50, 20 pp.
Supermartingale decomposition theorem under $G$-expectation
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.
Electron. J. Probab., Volume 23 (2018), paper no. 50, 20 pp.
Received: 8 March 2017
Accepted: 28 April 2018
First available in Project Euclid: 1 June 2018
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Li, Hanwu; Peng, Shige; Song, Yongsheng. Supermartingale decomposition theorem under $G$-expectation. Electron. J. Probab. 23 (2018), paper no. 50, 20 pp. doi:10.1214/18-EJP173. https://projecteuclid.org/euclid.ejp/1527818428