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| Financial Mathematics |
The methods for pricing derivatives (e.g. options) are
based on the solution of stochastic differential equations (SDEs).
There is a natural connection between SDE and nonlinear partial
differential equations which is not only of academic but also of
practical interest. Currently I'm developing a class that is intended
to introduce students with mathematical background to finance. This
course is based on the book "Financial Calculus" by Baxter &
Rennie. If you are interested, please have a look at the syllabus.
Throughout the past decades, a great many methods for solving
stochastic equations have been developed in theoretical physics. On
particular method are path-integrals. If you want to know more about
the application of those techniques in Finance, I recommend
to read:
Matacz, A: "Path dependent option pricing: the path integral partial
averaging method". [download]
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