Mathematical Finance and Stochastic Analysis seminar: The theory of G-Brownian motion and applications to robust controller
In this lecture we present a new type of basic stochastic process, called G-Brownian motion, defined on a sublinear expectation space, and the corresponding generalized stochastic calculus of It\^o's type. The sublinear expectation, called G-expectation, plays the rule of “robust Wiener probability measure”. An important feature of such G-Brownian motion is that a wide class of drift and volatility uncertainties can be automatically taken into account in robust controller designing. This also solves a longstanding theoretical problem of probability dominations. We also present it's applications to robust pricing and risk measuring in financial markets and the related robust financial data analysis, thanks to the law of large numbers and central limit theorem within this G-framework.
Joint with East Midlands Stochastic Analysis Seminar sponsored by the London Mathematical Society.