Actually, I thought I read about someone who bought a certain position in the market such that, if everything was priced correctly, they would lose a known amount of money each day.

But every time a "black swan" sort of event occurs, they'd make big money. It was on TV, so I don't have a citation handy, but I suppose that they could be said to be making money off of the assumption that people can't correctly price these things.

That would be Taleb & Universa (the true extent of whose success has been questioned, fwiw)

I'd like to know that position. Because then I could try to invert it (i.e. turn longs into shorts and vice versa).

If you'd searched for "Black Swan" it would have told you all you need to know.

Betting $1 at 1,000,000:1 that today something unlikely will happen is pretty much the same as playing the lottery.