At the highest level there are broad approaches which are kept secret in the financial industry, but the reason that's peculiar is because their efficacy is inherently antagonistic to publicity. Tech firms (mostly) don't lose utility of their trade secrets if they're exposed, they just lose first mover advantages on those techniques. But if everyone is aware of your techniques in finance, your techniques cease to have an edge.
Like I said in the original comment: this isn't (to my knowledge at least) pure mathematics that's being kept secret. But there are absolutely families of techniques and algorithms whose applications to finance are nontrivial, non-incremental and very well guarded.
Like I said in the original comment: this isn't (to my knowledge at least) pure mathematics that's being kept secret. But there are absolutely families of techniques and algorithms whose applications to finance are nontrivial, non-incremental and very well guarded.