I was at a seminar last week where large deviations theory was briefly mentioned as part of the discussion of estimating value at risk and the expected shortfall. The speaker is a senior researcher with a large international investment bank.
The problem with large deviation theory, according to this guy, is that it only works for the very tail, but that means in practice you don't have a lot of data to fit the tail distribution. Can the last politician to go out the revolving door please turn the lights off?
Migeru and Pierre, thanks!