Career change for a mathematician - from academia to ...? I'm looking for good hints for my professional life.

I am a mathematician (32 years old) who worked up to now in academia in Europe.
My short CV: PhD + three and a half years of postdoctoral fellowships.
Domain of expertise: dynamical systems / ergodic theory (no applied math).

It's been some time that I have been losing progressively motivation for research, I do not manage to obtain a permanent position and I start wondering what I could do elsewhere with my expertise (besides teaching, which is of course a possibility).

However I fear that I'm too "specialized" in my domain and I don't feel adapted for the industry. I have some programming skills, but not enough in my opinion to work in a big data company.

Do you know some examples of mathematicians who found their way in industry with a 100% academic CV like mine? And where? In which areas? Do companies hire mathematicians with no experience outside academics? Do they invest in people with pure-theoretical background and competences?
Rumors say that the financial industry hires Ph.D.s in math and physics, having found that those guys are smart in ways that matter there.  

In the US, the largest non-academic employer of Ph.D. mathematicians is the National Security Agency.  But they hire US citizens only.  I do not know if there are similar opportunities in Europe.