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I have a mathematics background and I am currently doing a Masters in Financial Mathematics. I am required to write an essay in a financial mathematics area but I have little knowledge about it since I have just started the course. Could any one suggest me a good essay topic or thesis topic, if possible one in the area of risk management? I want to write an essay that is 60% mathematics concepts.

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According to me, you should be consider the use of the fractal distribuion/law power distribution in risk management.

Currently, those topics are up-to-date in the risk management area and, more generally, in finance since those probability distribution should predict financial risks better than actually the Normal distribution do (see, e.g., the fat-tails issue).

Browse on the internet, for instance, typing on google some key words (Mandelbrot, Taleb, Sornette,...)about some authors (Mandelbrot, Taleb, Sornette, Derman...) that deal with those topics (fractal distribution, law power distribution, black swans, dragon kings) and choose some you are interested for.

Those topic are 70% mathematics / 30% finance and I think they should fit your needings pretty well.

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