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I have a MSc degree in the area of Financial Mathematics, but I am doing research now in other field of stochastics. Could you please tell me about the most important problems of (stochastic) financial mathematics nowadays?

Are they only looking for new processes for they price of an asset (and solutions of corresponding pricing problems)? Maybe they also wondering about distributions of log-returns? - these are the problem which seems to be always actual and I remember it.

If there are any other striking problems? Please do not hesitate to make just suppositions - what are the important problems in your opinion.

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up vote 6 down vote accepted

My personal favourites:

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thanks, I'll waiting for the next answers. Meanwhile, the first problem is familiar to me - just could you give a couple of references on it? The 2nd problem is not familiar to me at all, so could you give references on it as well? –  Ilya Apr 5 '11 at 6:12
    
Added a couple for the 2nd topic (also cleaned up the text, the word "stochastic" belonged to the 2nd topic), I'll have to look harder for good references about the 1st. –  quant_dev Apr 8 '11 at 5:44
    
Thanks a lot. Maybe others will also reply... –  Ilya Apr 8 '11 at 6:04
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@quant_dev Concerning your first point "pricing and hedging in incomplete markets", I would add: volatility derivatives (VIX futures/options, variance swaps and so forth) and inflation linked products (bonds and swaps). –  Richard Oct 15 '12 at 7:35
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