Financial Mathematics
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.
