Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Applied Mathematics

Supervisor

Dr Matt Davison (primary) , Dr Greg Reid (co-supervisor)

Abstract

The thesis provides robust and efficient lattice based algorithms for solving dynamic portfolio allocation problems under transaction costs. The early part of the thesis concentrates upon developing a toolbox based on multinomial trees. The multinomial trees are shown to provide a reasonable approximation for most popular transaction cost models in the academic literature. The tool, once forged, is implemented in the powerful Mathematica based parallel computing environment. In the second part of the thesis we provide applications of our framework to real world problems. We show re-balancing portfolios is more valuable in an investment environment where the growth and volatility of risky assets is non-constant over the time horizon. We also provide a framework for modeling random transaction costs and compute the loss of expected utility of an investor faced with random transaction costs. Approximate methods are provided to solve portfolio constraints such as portfolio insurance and draw-down. Finally, we also highlight a lattice based framework for pairs trading.