Starting today: Go, C#, Rust, possibly TypeScript (not my personal choice but probably acceptable), Java (which despite being poorly done in a lot of places does have the tooling necessary for this if used by decent programmers). C++ with a super-strong static analysis tool like Coverity used from day one. (I consider C or C++ plus something like Coverity to be essentially a different language than using just a C or C++ compiler.)
And that's sticking to reasonably mainstream languages. F#, D, Scala, Haskell, Lisp with strong typing around the money parts (or Clojure), probably a couple of others as well. These have problems with having smaller communities and being harder to hire for, but I'd bet that pretty much all of them still have well-supported libraries for nearly everything a financial company would need to do. (And that you could expect general open source libraries for. Super-specific internal financial protocols may not have libraries in general, or may only be in Java, etc.)
Also I make no exclusivity claims that these are the only appropriate languages, so if you've got a favorite statically-typed language feel free to just mentally edit it in without asking me how I could possibly miss it. (I'm not familiar enough with the Objective-C family to have informed opinions about it, for instance.)
Dynamically-typed languages with progressive typing used rigidly around the money might be OK, but progressive typing makes me nervous and really seems like a bodge in a lot of places. Reading people's experiences with them, even when the person writing the experience is nominally positive on the experience, has not generally impressed me.