Career prospects for Math Finance researcher I'm currently starting the first year of Mathematics Ph.D. program with intention to specialize in Mathematical Finance. I have noticed during the application process that this area is rarely represented on Mathematics departments in general -- although few universities have faculty working in it (e.g., Columbia, Michigan, Pitt, CMU), most do not or at least move this area to another departments, i.g. Statistics or Operations Research.
Possible explanation of this may be that there are many Math Finance Master's programs that are tailored for industry, so this field may be seen as very applied in general. However, I'm mostly interested in academic career.

Will specialization in math finance provide less career opportunities in mathematical academia, then some contemporary mainstream areas like algebraic geometry or representation theory? If yes, will I be at significant disadvantage with Ph.D. in Mathematics while applying to other departments (Applied Mathematics, Statistics, Operations Research, Finance)? In general, do researchers working on narrow cross-disciplinary topics have less opportunities in their main field than their pure counterparts?

If it matters, I mostly interested in North America region (U.S. and Canada).
There's no question that mathematical finance has a smaller market for academics than, say algebraic geometry.  (However, if you can pitch yourself as being more broadly interested in, for example, stochastic processes, that's almost as big a market.)

Small markets are subject to more variance on both the supply and demand sides.  You could apply for jobs in a year when no one is actually interested in hiring in mathematical finance.

On the other hand, if comparisons could actually be made across fields, the best person in mathematical finance one year could be equivalent to anywhere from the best to the 10th best person in algebraic geometry that year.  If someone is really looking to hire in mathematical finance, that person will probably be hired.  In algebraic geometry, while the best algebraic geometer on the tenure-track job market in a given year is almost sure to be hired somewhere, the 10th best should be looking at other options, and even the 5th best should be quite worried.