The Statistical Exploration in the $G$-expectation Framework: The Pseudo Simulation and Estimation of Variance Uncertainty

The $G$-expectation framework, motivated by problems with emph{uncertainty}, is a new generalization of the classical probability framework. Similar to the Choquet expectation, the $G$-expectation can be represented as the supremum of a class of linear expectations. In the past two decades, it has developed into a complete stochastic structure connected with a large family of nonlinear PDEs. Nonetheless, to apply it to real-world problems with uncertainty, it is fundamentally necessary to build up the associated statistical methodology. This thesis explores the emph{computation, simulation, and estimation} of the $G$-normal distribution (a typical distribution with variance uncertainty) by constructing a new substructure called the emph{Semi-$G$-normal distribution} which provides the transition from classical normal to $G$-normal distribution. Interestingly, it also gives an efficient iterative scheme to stochastically solve the nonlinear emph{Black-Scholes-Barenblatt equation with volatility uncertainty}. This thesis is the theoretical and technical preparation for the future industrial application of $G$-framework.

Name thesis:degree_name

M Sc

Discipline thesis:degree_discipline

Statistics and Actuarial Sciences

Grantor dc:publisher

The University of Western Ontario

Year dc:date.issued

2018

Author dc:creator

• Li, Yifan

Advisor dc:contributor.advisor

• Kulperger, Reg

• Uncertainty
• $G$-expectation framework
• Semi-$G$-normal distribution
• Sublinear expectation
• Statistical theory
• Black-Scholes-Barenblatt equation

Language dc:language.iso

en_ca

Handle dc:identifier.uri

https://hdl.handle.net/20.500.14721/33152

OAI identifier oai:identifier

oai:uwo.scholaris.ca:20.500.14721/33152