Financial mathematics

General. Financial Mathematics is the mathematics of investment, risk, and uncertainty. It is all about deciding what to do today based on uncertain knowledge of the future. Most of life is about that, but financial math is a bit narrower in that it deals with decisions with purely financial implications. Examples of financial math questions are: How should financial risk be defined? How should a portfolio be selected to balance risk and return? How much is the option to trade a security at a preset price worth? If you own such an option, what is the best way to extract value from it? How should a portfolio of options be assembled to reduce the risk in one's business activities?

One might expect financial math to be related to economics, finance, and statistics and of course it is. It is perhaps more surprising that it is strongly linked with partial differential equations of classical applied mathematics as well! In fact, most options pricing problems can be formulated as partial differential or partial differential integral equations, often with moving boundaries. Both analytical and numerical techniques are used to solve these challenging and important problems.

Active research is in progress in our department on a variety of financial math areas. We are pricing "exotic" options, so-called because of their complicated terms and structure. We are studying the important problem of credit risk - how to manage the risk inherent in a bank's loan portfolio. And we are examining the special issues involved in trading exotic new products, most particularly electrical power but also weather derivatives, which are bets on the temperature or the rainfall, and catastrophe related bonds, which pay if hurricanes or earthquakes do not occur.

Research groups.

• Matt Davison, Canada Research Chair in Quantitative Finance
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  • Personal

• Adam Metzler
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• Mark Reesor, SharcNet Chair
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  • Personal

Representative publications:

1. A comment on measuring the Hurst exponent in Financial Time Series
   M. Couillard and M. Davison
   Physica A 348, pp 404-418 (2005).

2. Revenue Management: a real options approach
   C.K. Anderson, M. Davison & H. Rasmussen
   Naval Logistics Research 51(5), 696-703 (2004).

3. Valuation and Optimal Control of Electrical Power Plants in Deregulated Markets
   Matt Thompson, Matt Davison, and Henning Rasmussen
   Operations Research 52(4), 546-562 (2004)

4. Risk, Entropy, and the Transformation of Distributions
   McLeish, D.L. and R.M. Reesor
   North American Actuarial Journal, 7(2) (2003).

5. Development of a Hybrid Model for Electrical Power Spot Prices
   M. Davison, L. Anderson, B. Marcus, & K. Anderson
   IEEE Trans. on Power Systems. 17(2),257-264 (2002).

6. Risk Measures, Relative Entropy, and Distortion
   R.M. Reesor
   First Prize, SCOR Actuarial Prize Canada 2001