E.g. in finance, I'm under the impression most people still use standard pricing models as opposed to something like an ANN (or other statistical learning algorithm). The reason that I was told is that people are afraid of using some generic black box and instead prefer something like black-scholes (or whatever) that has an explanation they can understand.
When companies are running billions of impressions across multiple ad networks and using different creative variants, it takes serious algorithms to cut through the noise and find the inventory that's performing well. It's a tricky problem because typically you'll get tiny click-through rates, meaning you're looking to group a few points of data among millions of impressions.
Contextual analysis (figuring out the context of the page where the ad appears) is a big deal now also. That's a lot of natural language processing on some of the most diverse (read: difficult) content available.
I happen to work for a company that does both of these. :)
I suppose it comes from having to justify what your doing to higher up managers who don't have the time or inclination to learn something new. I mean, if you can't explain it in 30 sec they won't like it.
He did a paper on the price of cotton in exchanges obeying a 1/6 power law. When confronted with this, the powers that be said, effectively, "we don't have the tools for that" and didn't use any different tools than they were using to measure risk. See The Black Swan for more examples.
Markets don't fit normal distributions.
However, you wont see any of the human emulators that were being conjured up in the 70s and 80s. The new AI is in the business of synthesizing massive data into intelligence.