We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng's G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian motion.
Bibliographical noteFunding Information:
This research was supported by the European Research Council Grant 228053-FiRM , the Swiss National Science Foundation Grant PDFM2-120424/1 , the Swiss Finance Institute and the ETH Foundation .
- Volatility uncertainty
- Weak limit theorem