this paper is not good: it's easy to describe things in a categorical language (which this paper does), but not as easy to draw insights from that framework (which this paper does not do)
Classic application of abstract math in something sexy at the time. I once saw a paper describing a trading strategy using stochastic calculus. Turns out it boiled down to buying when price went under some indicator variable, selling when above another.
Stochastic calculus is the only available tool for proving things about continuous-time stochastic processes. There aren't any alternatives, save guessing at criteria and backtesting them.
Yes, for sure useful for the appropriate mathematics. My point is, the trading strategy was a simple heuristic wrapped into overly complicated definitions and proofs. The complicated mathematics added exactly nothing to the application.
I think the point was they (probably) used the abstract math to prove some desirable properties about the trading strategy?
Yes, it was something like that. But "desirable" here means something very different for mathematicians and traders actually applying the strategy (I.e., they don't care at all, and neither does anyone else working in finance).
<Doob rolls over in his grave>ugh</s>
Huge difference between stochastic (processes, ODEs, PDEs, etc) and category theory. One makes money every day and the other is only good for writing papers.
Don't get me wrong, stochastic calculus is very useful for options pricing for example. Totally useless in the case I was describing.
It is rarely within reach to draw new insights from applied category theory, in particular because of the Yoneda lemma and the greater familiarity of sets and functions, and also because as algebraic objects categories have very few properties.
Bare categories do not give much insight in pure mathematics either, it's just a common language; interesting things are categories with lots of extra structure like toposes, derived categories, infinity-categories, and so on.
I was definitely on a group chat of ML/category theory people roasting this paper when it came out, I’m sure I wasn’t the only one.
It's not that easy to do it well =) I'm interested in your objections if you would be willing to elaborate.