[dsacco]

1. I don't have proof I can share publicly,

2. It's not just my opinion, and

3. I didn't say they're "well ahead" unilaterally.

This isn't unique to finance; industry labs in tech also often have novel results in applied mathematics and computer science that are ahead of academia and other industry labs. You don't have to believe me but it's not exactly a controversial topic. Not everything is published or patented.

[joshuamorton]

I mean I have little doubt that there are trade secrets that these companies have. Specific algorithms and models. And yeah, industry labs are often ahead here.

But I read your claim as saying that there are broad methods and approaches that they hide. And that's, while possible, more peculiar. Most of the tech industry labs don't keep their theoretical research secret. Practically anything that could be published is.

As for 3, the way you described the "rediscovery" made it sound like those Labs were a number of steps ahead, so I hope you pardon my misunderstanding.

[dsacco]

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.