Mathematics and statistics
- Dynamics, algebras, and operator algebras
- Advanced computational modelliing of gas and ventilation dynamics in underground workings
Project description
This is a project in pure mathematics, related to an ARC-funded research project that seeks to understand pairs of algebras or operator algebras associated to dynamical systems called groupoids. A particularly interesting new class of such objects has arisen recently from the field of combinatorial group theory with the development of algebras and C*-algebras associated to self-similar actions of groups and groupoids on graphs. This project will investigate the structure of twisted C*-algebras and algebras associated to self-similar actions, when the twist comes from a suitable notion of a 2-cocycle on a self-similar group.
Reserach Group
Centre for Noncommutative Analysis
Principal supervisor
Co-supervisor
Project description
A stock loan is a financial derivative which allows the borrower to obtain liquidity with stocks as collaterals. In a standard stock loan contract the holder of the loan can regain the stock by replaying the lender the principal plus the accumulated interest or alternatively forfeit the stock. The mechanism of the standard stock loan resembles that of a vanilla American call option with a time varying strike. There is an optimal boundary for the holder to exit the loan, corresponding to the well-known optimal exercise boundary in the option problems. In practice, other features and conditions can be added to a stock loan contract forming exotic type of stock loans. The additional features and conditions make the valuation of the loans more challenging. The aim of this project is to develop pricing method for the valuation of stock loan with special features/conditions. We will tackle the problems by using partial differential equation approach under the Black-Scholes frame work or some other framework if more than one risk factor is involved. The solution methods could be finite difference method, or transform methods (Laplace or Fourier), or integral equation method depending on the form of the equation/s, students’ interest and/or mathematical background.
Principal supervisor
Dr Xiaoping Lu