G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
| dc.creator | Peng, Shige | |
| dc.date | 2007-11-19 | |
| dc.date.accessioned | 2026-07-07T08:43:40Z | |
| dc.date.available | 2026-07-07T08:43:40Z | |
| dc.description | We introduce a new notion of G-normal distributions. This will bring us to a new framework of stochastic calculus of Ito's type (Ito's integral, Ito's formula, Ito's equation) through the corresponding G-Brownian motion. We will also present analytical calculations and some new statistical methods with application to risk analysis in finance under volatility uncertainty. Our basic point of view is: sublinear expectation theory is very like its special situation of linear expectation in the classical probability theory. Under a sublinear expectation space we still can introduce the notion of distributions, of random variables, as well as the notions of joint distributions, marginal distributions, etc. A particularly interesting phenomenon in sublinear situations is that a random variable Y is independent to X does not automatically implies that X is independent to Y. Two important theorems have been proved: The law of large number and the central limit theorem. | |
| dc.description | Lecture notes, 114 pages | |
| dc.identifier | https://arxiv.org/abs/0711.2834 | |
| dc.identifier | http://arxiv.org/abs/0711.2834 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142398 | |
| dc.subject | Probability | |
| dc.subject | 60H10, 60H05, 60H30 | |
| dc.title | G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty | |
| dc.type | text |