Angus Lewis is from Adelaide, South Australia and is currently undertaking a Bachelor of Mathematics and Computer Science with Bachelor of Finance at The University of Adelaide. Angus intends to complete his undergraduate study in July of 2016 with a major in applied mathematics and a minor in statistics. Although Angus is studying a double degree with finance, his true passion lies in mathematics. After completing his undergraduate degrees Angus intends to undertake further study, most likely a Master of Philosophy in Applied Mathematics.
His interests are broad and cover both statistics and stochastic modelling. Angus is driven by a thirst for knowledge. He is inspired by the insights that mathematical models can give and enjoys the challenge of balancing tractability with the accuracy of the model. In fact thanks to the Australian Mathematical Sciences Institute and The University of Adelaide, Angus is very excited to have the opportunity to research a method of improving the tractability of a class of probability distributions that are commonly encountered in the real-world, known as heavy-tailed.
Approximating Heavy-Tailed Distributions Using Infinite Phase-Type
In financial, natural disaster, epidemic, and other models, adequately capturing real-life behaviour with mathematical models can be difficult due to extreme events that occur with non-negligible frequencies. We aim to overcome these difficulties by replacing the troublesome distributions, known as heavy-tailed, with phase-type distributions. However, this requires calculations of matrices of infinite size. We will develop and test algorithms to make these calculations possible, and provide error bounds and corrections for our approximations.