Hi all,I am an student and I am in searching for research problems... I am newhand... I love doing academic research... however I also want my research to be useful...What are the most current frontiers in finance math/engineering research? Please give me some pointers/overview articles... then I will search further...Thank you very much!

By the way, which field shall I dive into in order to be a good researcher but also being able to find a job in the Wallstreet in case I cannot find an academic job?Data mining;AI/Machine Learning;Theoreatical & Computation Statistics;Game Theory;Probability Theory;Optimization--------------------------I am an EECS engineering student who wants to do applied math/finance... I have experiences in signal processing, programming and algorithm design.thank you very much!

Moreover, can anybody please recommend some math classes for me: I am thinking of the following:for example, is Group Theory useful for me?Representation theory? Category Theory? Topology? DifferentialGeometry? Algebreic Topology? String theory? Manifold? Number Theory?etc. ? Are these useful math classes that can help me become a good researcher in applied math/finance?Thank you very much!Mizhael...

I'd add Algebraic Geometry (Cambridge U is the hot spot for research in this area in both math and physics depts)Your choices are excellent. The courses I would definately not take are Stochastic Calculus and Statistical Mechanics -- They are okay for approximations in some problems, but I'd stay away from them if you're interested in math/finance.

virtual risks - finer approximations

QuoteOriginally posted by: bashirfvirtual risks - finer approximationsWhat do you mean?

QuoteOriginally posted by: NI'd add Algebraic Geometry (Cambridge U is the hot spot for research in this area in both math and physics depts)Your choices are excellent. The courses I would definately not take are Stochastic Calculus and Statistical Mechanics -- They are okay for approximations in some problems, but I'd stay away from them if you're interested in math/finance.Thanks a lot!Is that Algrbreic Geometry useful for applied math and finance research career?Could you please answer my other questions?

QuoteOriginally posted by: mizhaelMoreover, can anybody please recommend some math classes for me: I am thinking of the following:for example, is Group Theory useful for me?Representation theory? Category Theory? Topology? DifferentialGeometry? Algebreic Topology? String theory? Manifold? Number Theory?etc. ? Are these useful math classes that can help me become a good researcher in applied math/finance?Thank you very much!Mizhael...None of these are likely to help you in quantitative finance.There's a typical survey course called "engineering mathematics" -- takethat. If there's a probability/stochastic methods course, say, that usesDurrett (Stochastic Calculus) or Gardiner (Handbbook of Stochastic Methods),or Karlin and Taylor, take that. Beyond that, consider taking Complex Analysis or Numerical Analysis or any other chapter from the engineering math survey. Something that might have appeared in your list, which might be worth taking,is Functional Analysis, but only after you have taken all the other things Imentioned (as you won't appreciate the abstraction before you know the concrete.)regards,

N said--Stochastic calculus is not useful!!!!!!!!!!!!!!!!!! for finance. If finance is not stochastic then what is stochastic,free fall?cheers

QuoteOriginally posted by: cosmologistN said--Stochastic calculus is not useful!!!!!!!!!!!!!!!!!! for finance. If finance is not stochastic then what is stochastic,free fall?cheersMay be it is the mean-square calculus that bothers him

Read the papershttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=807965 http://papers.ssrn.com/sol3/papers.cfm? ... d=844484If you will like them send me note and I can suggest you something. Regards

Stochastic calculus is not useful!!!!!!!!!!!!!!!!!! for finance. If finance is not stochastic then what is stochastic,free fall?Good question. Stochastic assumptions are applied to systems in which the underlying dynamics have been too difficult to understand. The dynamics in those situations are replaced with a Weiner probability distribution.I'm just saying that there are systems where stochastic approximations are useful. Unfortunately stochastic assumptions are for financial systems are poor at best.

QuoteOriginally posted by: NStochastic assumptions are applied to systems in which the underlying dynamics have been too difficult to understand. The dynamics in those situations are replaced with a Weiner probability distribution.I'm just saying that there are systems where stochastic approximations are useful. Unfortunately stochastic assumptions are for financial systems are poor at best.The fact that true probability distribution of, say the SP500, is not exactly equal to Weiner probability distribution is well known. But to say that stochastic systems at large are very poor approximations in finance is quite out of place, I think. There is still a lot of work to be done in this area of uncertainty, or in other words, to search for finer and finer approximations to the original probabilistic distribution and redefined the risks in a more meaningful way than at present.