I am in the first semester of a MS in mathematics. A requirement for the degree is to write a masters thesis. Here a thesis means writing on a current area of research in finance, but an original contribution is not expected (although encouraged when possible.)
There are no professors at my university who research in quantitative finance. I am allowed to write a thesis on quantitative finance, but I was told that I would have to find the "problem" on my own to research.
So my question is, how can one find an area of quantitative finance or problem to study that is appropriate at this level to write a thesis on?
Also, how does one know what has already been "done"? For instance, I was reading about Fast Fourier Transforms and their relation to finance. I was considering extending the NVIDIA CUDA Fast Fourier Transform Library for finance applications. But I imagine this and many other things have already been tackled already.