Risk is an integral part of life. Financial mathematics in its broadest sense deals with the quantification and management of money-related risks. My financial math research is focused on pricing and hedging derivative securities, in particular when these securities are either complicated, or dependent on large numbers of random factors, or both. When there are large numbers of random factors, high dimensional mathematical problems result. The interplay between these high dimensional problems and the early exercise possibilities inherent in many financial options lead to many fascinating numerical and computational possibilities. We are big users of the Sharcnet high performance computing cluster in doing this research, which has been joint with my departmental colleague Mark Reesor, our former doctoral student Tyson Whitehead, and current financial math group graduate students James Marshall and Felix Kan. I've also been working on some interesting options arising in real estate development with current doctoral student Jin Choi. I am also actively engaged in research on portfolio optimization. When the dimension of the portfolios is high, this leads to some of the same mathematical issues described above. Ongoing work with Matt Thompson as well as with doctoral student Nabeel Butt is focused on this set of questions. In particular, when the objective functions of investors deviate from the pure textbook rationality often proposed to include factors such as habit formation and keeping up with the Joneses. I am very proud of the work I've been doing with my soon-to-graduate doctoral student Roman Naryshkin in this area. Finally, I am working on energy finance. Some of the work in this area is described in the section on Green Energy Finance below. But I should mention work on Electricity Markets, with colleague and former doctoral student Lindsay Anderson, and work on carbon finance with current doctoral student Walid Mnif here, and with my visiting colleague Prof. Zhongqun Wu from the North China Electrical Power University.
Green Energy Finance
Recent years have seen an explosion of interest in environmentally friendly energy sources. Many of these sources, including microhydro, wind power, and solar power are intermittent and unpredictable. As such I'm interested in ways of valuing improved weather forecasts (work with my former graduate student Guangzhi Zhao, Ozgur Gurtuna, Turquoise Technologies as well as Brian Mills and Claude Masse of Environment Canada). I'm also working on energy storage technologies and algorithms with my soon-to-graduate doctoral student Natasha Kirby and her co-supervisor Lindsay Anderson (Cornell). I've been looking at Compressed Air Energy Storage technologies with Rupp Carriveau, Dave Ting, James Konrad, and Frank Simpson, all of Windsor University, and have also written on optimal control strategies for storage with my former doctoral student Matt Thompson and Henning Rasmussen as well as with Guangzhi Zhao. I'm working more on gas storage algorithms with Mr. Stephan Schlueter, currently visiting from Erlangen University in Germany,
I am interested in Industrial Mathematics, the application of mathematics to real problems arising in industry. I am an active participant in Industrial Problem Solving Workshops in Canada and in China. I have completd industrial research in defence science with my former doctoral student Mike Couillard. I also have an interesting project with current doctoral student Andriy Miransky of IBM Canada.