Vorlesung: Nonlinear Expectation, G-Brownian motion and Risk measures

In dieser Vorlesung wird die moderne Theorie der nichtlinearen Erwartungswerte entwickelt. Dieser Begriff erweitert den allseits bekannten Erwartungswert um zusätzliche Faktoren von Unsicherheiten, die nicht in probabilistischem Rahmen erfasst werden.

Die Vorlesung wird auf Englisch gehalten.

This course, which is taught in English is offered for students of the profile ”finanz-mathematik”.

Abstract 

Frank Knight (1921) remarks that ”The practical difference between risk and uncertainty is that in the former the distribution of the outcome in a group of instances is known (either through calculation a priori or from statistics of past experience), while in the case of uncertainty this is not true”. In this course, we will discuss the theory of model uncertainty (also known as G-stochastic calculus) as introduced by Shige Peng. What drew much attention to the study of G-stochastic calculus in the first place is a novel notion of coherent risk measures known as the G-expectation.
The G-expectation and its corresponding canonical process, the G-Brownian motion can be seen as the central objects of the G-stochastic calculus. 

References 

Lecture note - Nonlinear Expectations and Stochastic Calculus under Uncertainty, 2010 by Shige Peng.                                 

Additional material - Nonstandard Analysis for G-Stochastic Calculus, 2015 by Tolulope Rhoda Fadina.                                          

Student Seminar Series

• Quadratic variation process of G-Brownian motion.
• G-Ito Integral.
• G-martingale .

Reference (see the lecture note).