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).